d/dx (sin^3 x) = d/dx (sinx sinx sinx)

Answer 1

use the chain rule
y = sin^3x
y' = 3 sin^2x cosx

Answer 2

d/dx (sinx sinx sinx)
=sin x d/dx(sin x sin x) + (sin x sin x) d/dx(sin x)
= sin x d/dx(sin x sin x) + (sin x sin x) cos x
= sin x[2sin x cos x] + sin^2 x cos x
= 2 sin^2 x cos x + sin^2 x cos x
= 3 sin^2 x cos x
which we knew anyway