# How do you find the derivative of y=cos(cosx) ?

Apr 5, 2018

$\frac{\mathrm{dy}}{\mathrm{dx}} = \sin x \cdot \sin \left(\cos x\right)$

#### Explanation:

First from the differentiation of trigonometric functions :

$\frac{d}{\mathrm{dx}} \cos x = - \sin x \mathrm{dx}$

$\frac{d}{\mathrm{dx}} \cos u = - \sin u \cdot \mathrm{du}$

Where $u$ is a function of $x$

so when You differentiate $y = \cos \left(\cos x\right)$

You get the following:

$\mathrm{dy} = - \sin \left(\cos x\right) \mathrm{dc} o s x$

which gives You:

$\mathrm{dy} = \left(- \sin \left(\cos x\right)\right) \cdot \left(- \sin x \cdot \mathrm{dx}\right)$

and by simpilification you get:

$\frac{\mathrm{dy}}{\mathrm{dx}} \cos x = \sin x \cdot \sin \left(\cos x\right)$