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Mathematics

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Calculus

Derivative

{wiki}

Here's an example of the chain rule. Suppose we want to calculate:
$$
\dv{}{x} e^{2x}
$$
So we have:
$$
f(x) = e^x \\
g(x) = 2x
$$
and so:
$$
f'(x) = e^x \\
g'(x) = 2
$$
Therefore the final result is:
$$
f'(g(x))g'(x) = e^{2x} 2 = 2 e ^{2x}
$$


Chain rule

Multivariable chain rule

{wiki}

If $f$ is differentiable at $a$ and $g$ is differentiable at $f(a)$, then
$$
(g\circ f)'(a)=g'(f(a))f'(a).
$$


{wiki=Chain_rule}

The chain rule is a fundamental concept in calculus used to differentiate composite functions.


Chain rule

Multivariable chain rule

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Chain rule

Multivariable chain rule

 Ancestors (5)

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 Articles by others on the same topic (2)

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