%% Derivative %%

Product Rule

Tags

Cegep1

Mathematics

Word count

40 words

Reading time

1 minute

Let $f$ and $g$ be two differentiable functions, then

$$\frac{d}{dx}(f(x)\cdot g(x))=f(x)g^{\prime }(x)+g(x)f^{\prime }(x)$$

The rule extends to >2 functions:

$$\frac{d}{dx}(f(x)g(x)h(x))=f^{\prime }(x)g(x)h(x)+g^{\prime }(x)f(x)h(x)+h^{\prime }(x)f(x)g(x)$$

Proof

Let $p(x)=f(x)g(x)$, then

Contributors

Ajitani Hifumi

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b6f0df6-Vault update: 2024-10-09T08:30:52