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

Question

24220 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-04-05T16:55:49

$\frac{d y}{d x} = sin x \cdot sin (cos x)$ $dy/dx=sinx*sin(cosx)$

First from the differentiation of trigonometric functions :

$\frac{d}{d x} cos x = - sin x d x$ $d/dx cosx=-sinxdx$

$\frac{d}{d x} cos u = - sin u \cdot d u$ $d/dxcosu=-sinu*du$

Where $u$ $u$ is a function of $x$ $x$

so when You differentiate $y = cos (cos x)$ $y=cos(cosx)$

You get the following:

$d y = - sin (cos x) d cos x$ $dy= -sin(cosx)dcosx$

which gives You:

$d y = (- sin (cos x)) \cdot (- sin x \cdot d x)$ $dy=(-sin(cosx))*(-sinx*dx)$

and by simpilification you get:

$\frac{d y}{d x} cos x = sin x \cdot sin (cos x)$ $dy/dxcosx=sinx*sin(cosx)$

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