Category:Examples of Use of Product Rule for Derivatives

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This category contains examples of use of Product Rule for Derivatives.

Let $\map f x, \map j x, \map k x$ be real functions defined on the open interval $I$.

Let $\xi \in I$ be a point in $I$ at which both $j$ and $k$ are differentiable.

Let $\map f x = \map j x \map k x$.


$\map {f'} \xi = \map j \xi \map {k'} \xi + \map {j'} \xi \map k \xi$

It follows from the definition of derivative that if $j$ and $k$ are both differentiable on the interval $I$, then:

$\forall x \in I: \map {f'} x = \map j x \map {k'} x + \map {j'} x \map k x$