Question

Find the derivative of sin^3 4x

Answer 1

I think it is 3sin^2(x)cos4

Answer 2

Use chain rule. You have that \[\frac{d}{dx}(\sin^3(4x)) = 3\sin^2(4x) \frac{d}{dx}(\sin(4x))\] \[=3\sin^2(4x)\cos(4x)\frac{d}{dx}(4x)=12\sin^2(4x)\cos(4x)\]