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Differentiation rules

{wiki=Chain_rule}

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


Chain rule

{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

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Chain rule

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