f(x) = (sin(x))^3. What is f'(x)

Write sin³(x) as sin²x*sinx and differentiate using product rule, u=sin²x, v=sinx, du/dx=2sinxcosx, dv/dx=cosx where the product rule is u(dv/dx) + v(du/dx). This gets 2sin²xcosx + sin²xcosx = 3sin²xcosx which is the correct answer