Calculus: Find the limit: $\lim_{h\rightarrow0}\frac{f(x+h)−f(x)}{h}$ given that $f(x)=\sin(2x)$ Find the limit:
$$\lim_{h\rightarrow0}\frac{f(x+h)−f(x)}{h}$$
Given that $f(x)=\sin(2x)$.
Tried many ways, but I kept on getting an indeterminate form. I can't find a way to cancel out terms on the numerator and denominator.
Any help will be appreciated.

Hint
$$\sin(2x+2h)=\sin 2x\cos 2h+\cos 2x\sin 2h$$
$$\lim_{u\to 0}{\sin u\over u}=1$$
$$\lim_{u\to 0}{\cos u-1\over u}=0$$
