Question

If `f(x) =sin(-x/4)` and `g(x) = sqrt(x^3+3`, what is `f'(g(x))`?

Answer 1

Below

Explanation:

`f(x)=sin(−x/4)`
`g(x)=sqrt(x^3+3)`

`f(g(x))=sin(−sqrt(x^3+3)/4)`

`f^'(g(x))=cos(−sqrt(x^3+3)/4)*-1/4*1/(2sqrt(x^3+3))*3x^2`

`f^'(g(x))=cos(−sqrt(x^3+3)/4)*(-3x^2)/(8sqrt(x^3+3))`