How to evaluate $\frac{d}{dx}\sin^2x$ I'm having trouble understanding how  $\frac{d}{dx}\sin^2x =2\sin(x)\cos(x)$.
Please show as many steps of the proof as necessary so that I can apply this to other problems.
Thank you for your time~! ^_^

We have that by the product rule,
$$\begin{align}\frac{d}{dx}\sin^2(x)&=\frac{d}{dx}(\sin(x)\sin(x))\\&=
(\frac{d}{dx}\sin(x))\sin(x)+\sin(x)(\frac{d}{dx}\sin(x))\\&=
\cos(x)\sin(x)+\sin(x)\cos(x)\\&=2\sin(x)\cos(x).\end{align}$$
