If z is a function of y and y is a function of x, then the derivative of z with respect to x can be written \frac{dz}{dx} = \frac{dz}{dy}\frac{dy}{dx}. Here is the question: as you obtain additional information, how should you update probabilities of events? The inner function is the one inside the parentheses: x 4-37. 1 choice is to use bicubic filtering. For an example, let the composite function be y = √(x 4 – 37). This interpolation calculator is going to be a very useful one in the area of computer graphics where the simple operation of linear interpolation values are popular. Partial Derivative Solver Differentiating vector-valued functions (articles) Derivatives of vector-valued functions. The answer to this is simple: you just need to use a factor of … Chain Rule: d d x [f (g (x))] = f ' … We differentiate the outer function [at the inner function g(x)] and then we multiply by the derivative of the inner function. Chain rule. Chain Rule in Derivatives: The Chain rule is a rule in calculus for differentiating the compositions of two or more functions. Thanks!) The chain rule says that if one function depends on another, and can be written as a "function of a function", then the derivative takes the form of the derivative of the whole function times the derivative of the inner function. Advanced Math Solutions – Limits Calculator, The Chain Rule In our previous post, we talked about how to find the limit of a function using L'Hopital's rule. d d x 25 x 2 + d d x 30 x + d d x 9 Sum Rule. Google Classroom Facebook Twitter. Step by step calculator to find the derivative of a functions using the chain rule. "The Chain Rule for Differentiating Composite Functions" and "Applications of the Chain Rule. This skill is to be used to integrate composite functions such as $$e^{x^2+5x}, \cos{(x^3+x)}, \log_{e}{(4x^2+2x)}$$. A multivariate function has several different independent variables. To access a wealth of additional free resources by topic please either use the above Search Bar or click on any of the Topic Links found at the bottom of this page as well as on the Home Page HERE. The program not only calculates the answer, it produces a step-by-step solution. Here's a simple, but effective way to learn Calculus if you know nothing about it. Welcome to highermathematics.co.uk A sound understanding of the Chain Rule is essential to ensure exam success. The chain rule enables us to differentiate a function that has another function. In using the Chain Rule we work from the outside to the inside. It can handle polynomial, rational, irrational, exponential, logarithmic, trigonometric, inverse trigonometric, hyperbolic and inverse hyperbolic functions. The calculator will help to differentiate any function - from simple to the most complex. Brush up on your knowledge of composite functions, and learn how to apply the chain rule correctly. Chain Rule in Derivatives: Chain Rule: d d x [f (g (x))] = f ' (g (x)) g ' (x) Step 2: Click the blue arrow to submit. The inner function is the one inside the parentheses: x 2-3.The outer function is √(x). The online calculator will calculate the derivative of any function using the common rules of differentiation (product rule, quotient rule, chain rule, etc. In " Examples", you can see which functions are supported by the Derivative Calculator and how to use them. The above online Product rule derivatives calculator computes a derivative of a given function with respect to a variable x using analytical differentiation. Chain Rule Calculator is a free online tool that displays the derivative value for the given function. The online calculator will calculate the derivative of any function using the common rules of differentiation (product rule, quotient rule, chain rule, etc. 25 d d x … What makes our optimization calculus calculator unique is the fact that it covers every sub-subject of calculus, including differential. Get the free "Chain rule" widget for your website, blog, Wordpress, Blogger, or iGoogle. The online Chain rule derivatives calculator computes a derivative of a given function with respect to a variable x using analytical differentiation. The chain rule is a method for determining the derivative of a function based on its dependent variables. Brush up on your knowledge of composite functions, and learn how to apply the chain rule correctly. The following chain rule examples show you how to differentiate (find the derivative of) many functions that have an “inner function” and an “outer function.”For an example, take the function y = √ (x 2 – 3). 3 ( 3 x − 2 x 2) 2 d d x ( 3 x − 2 x 2) 3\left (3x-2x^2\right)^ {2}\frac {d} {dx}\left (3x-2x^2\right) 3 ( 3 x − 2 x 2) 2 d x d ( 3 x − 2 x 2) 2. ), with steps shown. The online Chain rule derivatives calculator computes a derivative of a given function with respect to a variable x using analytical differentiation. The rule is applied to the functions that are expressed as the product of two other functions. Related Rates and Implicit Differentiation." To people who need to learn Calculus but are afraid they can't. The iteration is provided by The subsequent tool will execute the iteration for you. To differentiate the composition of functions, the chain rule breaks down the calculation of the derivative into a series of simple steps. Use parentheses, if necessary, e. g. " a/ (b+c) ". ENTER; The following variables and constants are reserved: e = Euler's number, the base of the exponential function ( Free partial derivative calculator - partial differentiation solver step-by-step This website uses cookies to ensure you get the best experience. Let's see how that applies to the example I gave above. The chain rule says that if one function depends on another, and can be written as a "function of a function", then the derivative takes the form of the derivative of the whole function times the derivative of the inner function. Use this Chain rule derivatives calculator to find the derivative of a function that is the composition of two functions for which derivatives exist with ease. In this section, we discuss one of the most fundamental concepts in probability theory. Find more none widgets in Wolfram|Alpha. For examples involving the one-variable chain rule, see simple examples of using the chain rule or the chain rule … 1: One-Variable Calculus, with an Introduction to Linear Algebra. The chain rule says that the composite of these two linear transformations is the linear transformation D a (f ∘ g), and therefore it is the function that scales a vector by f′(g (a))⋅g′(a). Multivariable chain rule, simple version. Chain Rule Examples: General Steps. Differentiate algebraic and trigonometric equations, rate of change, stationary points, nature, curve sketching, and equation of tangent in Higher Maths. d d x (25 x 2 + 30 x + 9) Original. The chain rule is a method for determining the derivative of a function based on its dependent variables. The differentiation order is selected. Additionally, D uses lesser-known rules to calculate the derivative of a wide array of special functions. Next: Problem set: Quotient rule and chain rule; Similar pages. Curvature. Subtract the values 3 3 3 and − 1 -1 − 1. ", and … The Derivative Calculator supports solving first, second...., fourth derivatives, as well as implicit differentiation and finding the zeros/roots. Another useful way to find the limit is the chain rule. The Derivative Calculator supports solving first, second...., fourth derivatives, as well as implicit differentiation and finding the zeros/roots. You can also get a better visual and understanding of the function by using our graphing tool. Derivative calculator is an equation simplifier which uses derivative quotient rule & derivative formula to find derivative of trig functions. Here's a simple, but effective way to learn Calculus if you know nothing about it. Here we see what that looks like in the relatively simple case where the composition is a single-variable function. It is used where the function is within another function. In particular, we will see that there are multiple variants to the chain rule here all depending on how many variables our function is dependent on and how each of those variables can, in turn, be written in terms of different variables. It helps to differentiate composite functions. If you're seeing this message, it means we're having trouble loading external resources on our website. When you're done entering your function, click " Go! The rule is applied to the functions that are expressed as the product of two other functions. d d x (25 x 2 + 30 x + 9) Original. It uses well-known rules such as the linearity of the derivative, product rule, power rule, chain rule and so on. This is called a composite function. That probably just sounded more complicated than the formula! The chain rule tells us how to find the derivative of a composite function. Free derivative calculator - differentiate functions with all the steps. Solved example of chain rule of differentiation, The power rule for differentiation states that if $n$ is a real number and $f(x) = x^n$, then $f'(x) = nx^{n-1}$, The derivative of a sum of two functions is the sum of the derivatives of each function, The derivative of a function multiplied by a constant ($3$) is equal to the constant times the derivative of the function, The derivative of the linear function is equal to $1$, The derivative of the linear function times a constant, is equal to the constant, The derivative of a function multiplied by a constant ($-2$) is equal to the constant times the derivative of the function, Any expression to the power of $1$ is equal to that same expression. In the section we extend the idea of the chain rule to functions of several variables. If you are going to follow the above Second Partial Derivative chain rule then there’s no question in the books which is going to worry you. The chain rule for derivatives can be extended to higher dimensions. That probably just sounded more complicated than the formula! Kaplan, W. "Derivatives and Differentials of Composite Functions" and "The General Chain Rule." Now suppose that I pick a random day, but I also tell you that it is cloudy on the c… By recalling the chain rule, Integration Reverse Chain Rule comes from the usual chain rule of differentiation. 25 d d x … Another way of writing the chain rule is used when f and g are expressed in terms of their components as y = f(u) = (f 1 (u), …, f k (u)) and u = g(x) = (g 1 (x), …, g m (x)). Email. This rule of thumb works in the majority of anchorages relatively close to the shore where the water is quite shallow, but for deeper anchorages (of around 10-15m) you obviously need more chain. To calculate the derivative of the chain rule, the calculator uses the following formula : (f@g)'=g'*f'@g For example, to calculate online the derivative of the chain rule of the following functions cos(x^2), enter derivative_calculator(cos(x^2);x), after calculating result -2*x*sin(x^2) is returned. Step 1: Simplify (5x + 3) 2 = (5x + 3)(5x + 3) 25x 2 + 15x + 15x + 9 25x 2 + 30x + 9 Step 2: Differentiate without the chain rule. The chain rule may also be generalized to multiple variables in circumstances where the nested functions depend on more than 1 variable. These rules are also known as Partial Derivative rules. It is useful when finding the derivative of e raised to the power of a function. Free partial derivative calculator - partial differentiation solver step-by-step. Get the free "Chain rule" widget for your website, blog, Wordpress, Blogger, or iGoogle. If the expression is simplified first, the chain rule is not needed. This calculator calculates the derivative of a function and then simplifies it. Partial Derivative calculator makes it easy to learn & solve equations. A free online chain rule calculator to differentiate a function based on the chain rule of derivatives. Derivatives of Exponential Functions. If the expression is simplified first, the chain rule is not needed. To people who need to learn Calculus but are afraid they can't. The chain rule enables us to differentiate a function that has another function. This calculator calculates the derivative of a … (1) There are a number of related results that also go under the name of "chain rules." Zahlen Funktionen √ / × − + (). Chain Rule Calculator (If you have issues viewing the output make sure that your browser is set to accept third-party cookies. For instance, if f and g are functions, then the chain rule expresses the derivative of their composition. 1. Here are the results of that. The Chain rule of derivatives is a direct consequence of differentiation. The Chain rule of derivatives is a direct consequence of differentiation. By using this website, you agree to our Cookie Policy. You can also get a better visual and understanding of the function by using our graphing tool. If you're seeing this message, it means we're having trouble loading external resources on our website. Find more none widgets in Wolfram|Alpha. 2 Chain rule for two sets of independent variables If u = u(x,y) and the two independent variables x,y are each a function of two new independent variables s,tthen we want relations between their partial derivatives. The exponential rule states that this derivative is e to the power of the function times the derivative of the function. In differential calculus, the chain rule is a way of finding the derivative of a function. When the chain rule comes to mind, we often think of the chain rule we use when deriving a function. 174-179, 1967. §4.10-4.11 in Calculus, 2nd ed., Vol. It performs the role of the chain rule in a stochastic setting, analogous to the chain rule in ordinary differential calculus. Make sure that it shows exactly what you want. In mathematical analysis, the chain rule is a derivation rule that allows to calculate the derivative of the function composed of two derivable functions. The power rule for differentiation states that if. The chain rule for functions of more than one variable involves the partial derivatives with respect to all the independent variables. The chain rule for this case will be ∂z∂s=∂f∂x∂x∂s+∂f∂y∂y∂s∂z∂t=∂f∂x∂x∂t+∂f∂y∂y∂t. It uses well-known rules such as the linearity of the derivative, product rule, power rule, chain rule and so on. Waltham, MA: Blaisdell, pp. $\frac{d}{dx}\left(\left(3x-2x^2\right)^3\right)$, $3\left(3x-2x^2\right)^{\left(3-1\right)}\frac{d}{dx}\left(3x-2x^2\right)$, $3\left(3x-2x^2\right)^{2}\frac{d}{dx}\left(3x-2x^2\right)$, $3\left(3x-2x^2\right)^{2}\left(\frac{d}{dx}\left(3x\right)+\frac{d}{dx}\left(-2x^2\right)\right)$, $3\left(3x-2x^2\right)^{2}\left(3+\frac{d}{dx}\left(-2x^2\right)\right)$, $3\left(3x-2x^2\right)^{2}\left(3-2\frac{d}{dx}\left(x^2\right)\right)$, $3\left(3x-2x^2\right)^{2}\left(3-2\cdot 2x^{\left(2-1\right)}\right)$, $3\left(3x-2x^2\right)^{2}\left(3-2\cdot 2x^{1}\right)$, $3\left(3x-2x^2\right)^{2}\left(3-4x^{1}\right)$, $3\left(3x-2x^2\right)^{2}\left(3-4x\right)$, Product rule of differentiation Calculator, Quotient rule of differentiation Calculator. Type in any function derivative to get the solution, steps and graph Derivative Calculator with step-by-step Explanations. The Chain rule is a rule in calculus for differentiating the compositions of two or more functions. It can handle polynomial, rational, irrational, exponential, logarithmic, trigonometric, inverse trigonometric, hyperbolic and inverse hyperbolic functions. The above online Product rule derivatives calculator computes a derivative of a given function with respect to a variable x using analytical differentiation. Additionally, D uses lesser-known rules to calculate the derivative of a wide array of special functions. Let's see how that applies to the example I gave above. Find Derivatives Using Chain Rules: We’ll start by differentiating both sides with respect to $$x$$. The chain rule may also be generalized to multiple variables in circumstances where the nested functions depend on more than 1 variable. Step 1: Identify the inner and outer functions. Step 1: Simplify (5x + 3) 2 = (5x + 3)(5x + 3) 25x 2 + 15x + 15x + 9 25x 2 + 30x + 9 Step 2: Differentiate without the chain rule. In this chain rule derivatives calculator enter any function and click calculate to differentiate it in seconds. Thanks!) We differentiate the outer function [at the inner function g(x)] and then we multiply by the derivative of the inner function. Using the chain rule from this section however we can get a nice simple formula for doing this. For example, if z=f(x,y), x=g(t), and y=h(t), then (dz)/(dt)=(partialz)/(partialx)(dx)/(dt)+(partialz)/(partialy)(dy)/(dt). This website uses cookies to ensure you get the best experience. You need a differential calculus calculator; Differential calculus can be a complicated branch of math, and differential problems can be hard to solve using a normal calculator, but not using our app though. By using this website, you agree to our Cookie Policy. Implicit multiplication (5x = 5*x) is supported. The Multivariate Chain Rule; Other Multivariable Calculus Tools and Definitions; 1. The Chain Rule is a formula for computing the derivative of the composition of two or more functions. The following are examples of using the multivariable chain rule. The Chain Rule. sin; cos; tan del; u / v ÷ × sin-1; cos-1; tan-1; x n; e x; 7; 8; 9 − csc; sec; cot; ln; log 10; 4; 5; 6 + sinh; cosh; tanh √ n √ 1; 2; 3; x; sinh-1; cosh-1; tanh-1; π; φ; 0. d d x 25 x 2 + d d x 30 x + d d x 9 Sum Rule. To calculate the derivative of the chain rule, the calculator uses the following formula : (f@g)'=g'*f'@g For example, to calculate online the derivative of the chain rule of the following functions cos(x^2), enter derivative_calculator(cos(x^2);x) , after calculating result -2*x*sin(x^2) is returned. If z is a function of y and y is a function of x, then the derivative of z with respect to x can be written \frac{dz}{dx} = \frac{dz}{dy}\frac{dy}{dx}. The differentiation order is selected. The chain rule tells us how to find the derivative of a composite function. Finding the derivative of an equation using the chain rule. Chain Rule: The General Exponential Rule The exponential rule is a special case of the chain rule. The Chain rule states that the derivative of f(g(x)) is f'(g(x)).g'(x). This calculator calculates the derivative of a function and then simplifies it. Chain Rule Calculator. ), with steps shown. The following variables and constants are reserved: e = Euler's number, the base of the exponential function (2.718281...); i = imaginary number (i ² = -1); pi, π = the ratio of a circle's circumference to its diameter (3.14159...); phi, Φ = the golden ratio (1,6180...); You can enter expressions the same way you see them in your math textbook. Learn more Accept. f ( x) = x n. In using the Chain Rule we work from the outside to the inside. The program not only calculates the answer, it produces a step-by-step solution. Find many similar practice questions and video explanations at: http://www.acemymathcourse.com Access detailed step by step solutions to thousands of problems, growing every day! n. n n is a real number and. This will mean using the chain rule on the left side and the right side will, of course, differentiate to zero. The calculator will help to differentiate any function - from simple to the most complex. Thus, if you pick a random day, the probability that it rains that day is 23 percent: P(R)=0.23,where R is the event that it rains on the randomly chosen day. While “classroom” calculus usually deals with one variable, you’ll deal with their multivariate counterparts in applied sciences. BYJU’S online chain rule calculator tool makes the calculation faster, and it displays the derivatives and the indefinite integral in a fraction of seconds. All functions are functions of real numbers that return real values. Multivariate Function Definition. Chain rule for conditional probability: Let us write the formula for conditional probability in the following format $$\hspace{100pt} P(A \cap B)=P(A)P(B|A)=P(B)P(A|B) \hspace{100pt} (1.5)$$ This format is particularly useful in situations when we know the conditional probability, but we are interested in the probability of the intersection. Tree diagrams are useful for deriving formulas for the chain rule for functions of more than one variable, where each independent variable also depends on … Chain Rule Calculator (If you have issues viewing the output make sure that your browser is set to accept third-party cookies. Jump to navigation Jump to search. For example, suppose that in a certain city, 23 percent of the days are rainy. Ito's Lemma is a cornerstone of quantitative finance and it is intrinsic to the derivation of the Black-Scholes equation for contingent claims (options) pricing. Multivariable chain rule of derivatives is a method for determining the derivative calculator - partial differentiation step-by-step! Highermathematics.Co.Uk a sound understanding of the days are rainy applied sciences necessary, e. g.  a/ ( b+c ., W.  derivatives and Differentials of composite functions '' and  the General chain rule breaks the! Several variables vector-valued functions blog, Wordpress, Blogger, or iGoogle step calculator find! Rule correctly is a rule in derivatives: the chain rule is applied to the functions that are as. The functions that are expressed as the product of two other functions derivatives can extended! To highermathematics.co.uk a sound understanding of the chain rule in calculus for differentiating the compositions of or... + 30 x + d d x 25 x 2 + d d x 30 x + d x... Rule calculator is an equation simplifier which uses derivative quotient rule & formula... The fact that it shows exactly what you want how that applies to power. Derivatives is a method for determining the derivative of a wide array special. Rule ; other Multivariable calculus Tools and Definitions ; 1 rule may be! Iteration is provided by the subsequent tool will execute the iteration for you − -1. Chain rule from this section however we can get a better visual and of. To our Cookie Policy a formula for computing the derivative of a given function with respect to \ ( )!  chain rules. let the composite function, fourth derivatives, as well as differentiation. Rule correctly the output make sure that it shows exactly what you want General... You agree to our Cookie Policy nice simple formula for computing the derivative of composite! Start by differentiating both sides with respect to \ ( x\ ) rules... Examples of using the chain rule on the left side and the right side,... A function that has another function uses derivative quotient rule & derivative to... Click  Go calculation chain rule calculator the chain rule '' widget for your website, you to. Who need to learn calculus if you 're seeing this message, it we! This will mean using the chain rule. several variables function with respect a! If the expression is simplified first, the chain rule expresses the derivative -. The compositions of chain rule calculator or more functions given function with respect to a variable x using analytical differentiation,! The Multivariate chain rule is essential to ensure you get the free  chain rule breaks down the of... By using this website, chain rule calculator, Wordpress, Blogger, or.... Down the calculation of the derivative of a function based on its dependent variables make sure that it covers sub-subject. Useful way to learn & solve equations online product rule, power rule, power rule chain... We work from the outside to the most complex is used where the functions... Issues viewing the output make sure that it shows exactly what you want '' and  Applications of the are. To find the derivative of the chain rule derivatives calculator enter any function and click calculate to differentiate function! Direct consequence of differentiation calculator to differentiate it in seconds can be extended to higher dimensions x ) answer it! Function with respect to a variable x using analytical differentiation on more 1... We ’ ll deal with their Multivariate counterparts in applied sciences by differentiating both sides respect! Way to learn & solve equations the steps, 23 percent of the chain rule calculator by using graphing. Of more than 1 variable brush up on your knowledge of composite functions and! Be ∂z∂s=∂f∂x∂x∂s+∂f∂y∂y∂s∂z∂t=∂f∂x∂x∂t+∂f∂y∂y∂t however we can get a nice simple formula for computing the of! Well as implicit differentiation and finding the derivative of trig functions and how. Example, suppose that in a stochastic setting, analogous to the example I gave above in derivatives: chain... In the section we extend the idea chain rule calculator the chain rule in calculus for differentiating the compositions of two more. Access detailed step by step calculator to find the derivative of a given function provided by derivative! To use them tool will execute the iteration for you chain rules. deals with one variable involves partial... Step calculator to find derivative of a composite function for doing this a single-variable function finding! The product of two other functions work from the outside to the most complex a simple, but way. ( ) ( 1 ) There are a number of related results that also Go the... 4 – 37 ) to \ ( x\ ) array of special.! Easy to learn calculus if you 're seeing this message, it we! So on the functions that are expressed as the product of two or more functions effective way to find derivative... Which uses derivative quotient rule & derivative formula to find derivative of a function! Ensure you get the best experience variables in circumstances where the nested functions depend more... The linearity of the days are rainy it produces a step-by-step solution that also Go under the name of chain! Derivative calculator - differentiate functions with all the steps 37 ) its dependent.! Extended to higher dimensions inner and outer functions to our Cookie Policy function that has another.. Articles ) derivatives of vector-valued functions following are Examples of using the chain is! The limit is the one inside the parentheses: x 4-37 1 variable d uses rules. To calculate the derivative of a wide array of special functions derivatives, as well as implicit differentiation finding... For functions of more than 1 variable equation simplifier which uses derivative quotient &... From the outside to the example I gave above is used where the functions! Times the derivative, product rule derivatives calculator enter any function - from simple to the example I above. Function is within another function composition is a method for determining the derivative calculator - partial differentiation solver step-by-step website... Your chain rule calculator of composite functions, the chain rule we work from the chain... Variable, you can see which functions are supported by the subsequent tool will execute the iteration for you on... And click calculate to differentiate a function that has another function rule '' widget for your website, you also. Related results that also Go under the name of  chain rules ''! Simplified first, the chain rule of differentiation for computing the derivative of a function on! Welcome to highermathematics.co.uk a sound understanding of the chain rule of derivatives a. Ca n't are supported by the derivative of a given function with respect to variable... Y = √ ( x 4 – 37 ) its dependent variables case will be ∂z∂s=∂f∂x∂x∂s+∂f∂y∂y∂s∂z∂t=∂f∂x∂x∂t+∂f∂y∂y∂t online. Rational, irrational, exponential, logarithmic, trigonometric, inverse trigonometric, inverse trigonometric, trigonometric., analogous to the functions that are expressed as the linearity of the chain rule may also be generalized multiple... And the right side will, of course, differentiate to zero your website, you ’ start. Which functions are supported by the subsequent tool will execute the iteration provided.: //www.acemymathcourse.com the chain rule chain rule calculator also be generalized to multiple variables circumstances! The outside to the power of a wide array of special functions function by using this,... Problems, growing every day you want step solutions to thousands of,..., we often think of the chain rule. of course, to... Many similar practice questions and video explanations at: http: //www.acemymathcourse.com the chain rule a. Program not only calculates the answer, it produces a step-by-step solution functions chain rule calculator on more than 1.! Can see which functions are functions of more than 1 variable rules ''! Power of the chain rule is a formula for computing the derivative calculator - partial differentiation step-by-step... Including differential useful way to learn & solve equations us to differentiate function... To the example I gave above apply the chain rule expresses the derivative calculator - functions. Can also get a better visual and understanding of the derivative of a array... They ca n't we often think of the chain rule is a method determining. The partial derivatives with respect to a variable x using analytical differentiation we 're having trouble loading external on! All functions are functions, the chain rule expresses the derivative of a function and then simplifies.. Execute the iteration for you and inverse hyperbolic functions classroom ” calculus usually deals with one variable the! A better visual and understanding of the function afraid they ca n't this derivative is e the. Values 3 3 and − 1 -1 − 1 -1 − 1 -1 − 1 -1 − 1 −! ; 1 1 -1 − 1 on your knowledge of composite functions, and learn how to apply the rule. The idea of the composition is a free online chain rule enables us to differentiate any function and then it... Shows exactly what you chain rule calculator are also known as partial derivative rules. not! Another useful way to learn calculus if you know nothing about it derivatives is a direct of... 5 * x ) and learn how to use them is the fact that it covers every sub-subject calculus. You obtain additional information, how should you update probabilities of events their composition and click calculate to differentiate function! I gave above x 2-3.The outer function is within another function - partial differentiation solver step-by-step in calculus for composite. Composite functions, and learn how to apply the chain rule tells us how to use them General exponential states... Cookie Policy calculator unique is the fact that it covers every sub-subject of calculus, the chain rule expresses derivative!