Math Doubts

Chain Rule

Formula

$\dfrac{d}{dx} {f[{g(x)}]} \,=\, {f'[{g(x)}]}.{g'{(x)}}$

A formula that calculates the derivative of the composition of two or more functions is called the chain rule.

Introduction

$f{(x)}$ and $g{(x)}$ are two functions in terms of $x$ but $f{(g{(x)})}$ is a function, formed by the composition of both functions. Actually, the derivative each function can be calculated directly in calculus by the differentiation rules but the differentiation of composition of two or more functions cannot be calculated directly due to the complexity of the function.

So, chain rule is the only way to find the derivative of the composition of two or more functions. So, learn the proof of chain rule firstly and then, understand the use of chain rule in differential calculus.

Proof

Learn how to prove the chain rule in differential calculus mathematically.

Examples

List of examples to understand how to use chain rule for functions which contain two or more functions internally.

Problems

Learn how to solve derivative of the composition of two or more functions by chain rule.



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