Question

What is the derivative of `cos( sin( x ))`?

Answer 1

`(dy)/(dx)=-sin(sin(x))cos(x)`

Explanation:

`d/(dx)cos(sin(x))`

Using chain rule, `(dy)/(dx)=(dy)/(du)*(du)/(dx)`, let `u=sin(x)`

`(dy)/(du)=d/(du)cosu=-sinu=-sin(sin(x))`

`(du)/(dx)=d/(dx)sin(x)=cos(x)`

`:.(dy)/(dx)=-sin(sin(x))*cos(x)=-sin(sin(x))cos(x)`