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What is the derivative of $C\,f(x)$ where $C$ is a constant and $f(x)$ is differentiable.

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Lesson Parent:

Problem:

Show that
$\frac{d}{dx}\left[C\,f(x)\right]=C\,\frac{df}{dx}.$

Answer:

$C\,\frac{df}{dx}$

Solution:

If <Sign in to see all the formulas> where $C$ is a constant and $f(x)$ is differentiable then

Because $f(x)$ is differentiable we know that

Furthermore, we know that

where

$K$ is a constant and

Therefore,