How do you differentiate # Sin ^ 3 x#?

1 Answer
Jul 13, 2016

#dy/dx = 3sin^2(x) *cos x#

Explanation:

In order to differentiate #sin^3(x)#, we need to use a chain rule, which tells us that

#d/dx[f(g(x))] = f'(g(x))*g'(x)#

Letting #y = sin^(3)(x)#, then

#dy/dx = 3sin^2(x) *cos x#

In this problem, we've also performed the power rule, namely by subtracting #1# from the power of #3# on the #sin x# term, which is why we end up with a #sin^2(x)#.