Question

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

Answer 1

`f'(x)=-sec^2xsin(tanx)cos(cos(tanx))`

Explanation:

`f(x)=sin(g(x))`
`f'(x)=g'(x)cos(g(x))`

`g(x)=cos(h(x))`
`g'(x)=-h'(x)sin(h(x))`

`h(x)=tan(x)`
`h'(x)=sec^2x`

`g'(x)=-sec^2xsin(tanx)`
`g(x)=cos(tanx)`

`f'(x)=-sec^2xsin(tanx)cos(cos(tanx))`