Question

Question #cafe0

Answer 1

`d/dx(cos^{3}(x))=3cos^{2}(x)*(-sin(x))=-3cos^{2}(x)sin(x)`

Explanation:

Use the Chain Rule `d/dx(f(g(x)))=f'(g(x))*g'(x)` with `f(x)=x^{3}` and `g(x)=cos(x)`.

Since `f'(x)=3x^{2}` and `g'(x)=-sin(x)`, the answer follows.