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Here's an example of the chain rule. Suppose we want to calculate:

\frac{d}{d x} e^{2 x}

So we have:

f (x) = e^{x} g (x) = 2 x

and so:

f^{'} (x) = e^{x} g^{'} (x) = 2

Therefore the final result is:

f^{'} (g (x)) g^{'} (x) = e^{2 x} 2 = 2 e^{2 x}

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

Barack Obama 11 Created 2023-01-13 Updated 2025-04-18

Chain rule