Question

If `f(x)= sin(- x -1)` and `g(x) = 4x^2 -5`, how do you differentiate `f(g(x))` using the chain rule?

Answer 1

`d/dx(f[g(x)])=-8xcos(5-4x^2)`

Explanation:

`f[g(x)]=f(4x^2-5)`

`=sin[-(4x^2-5)]`

`=sin(5-4x^2)`

`therefore d/dx[sin(5-4x^2)]=-8xcos(5-4x^2)`