# How do you differentiate f(x)=sec(8x )  using the chain rule?

Jan 22, 2016

Please see the explanation section, below.

#### Explanation:

We know that $\frac{d}{\mathrm{dx}} \left(\sec x\right) = \sec x \tan x$

Applying the chain rule, we have

$\frac{d}{\mathrm{dx}} \left(\sec u\right) = \sec u \tan u \frac{\mathrm{du}}{\mathrm{dx}}$

So, in this question, since $u = 8 x$, we get

$f ' \left(x\right) = \sec \left(8 x\right) \tan \left(8 x\right) \frac{d}{\mathrm{dx}} \left(8 x\right)$

$= 8 \sec \left(8 x\right) \tan \left(8 x\right)$