Question #cafe0

1 Answer
Oct 24, 2017

d/dx(cos^{3}(x))=3cos^{2}(x)*(-sin(x))=-3cos^{2}(x)sin(x)ddx(cos3(x))=3cos2(x)(sin(x))=3cos2(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.