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.

Use http://mathworld.wolfram.com/ProsthaphaeresisFormulas.html
$$\sin2a(x+h)-\sin2ax=2\sin(ah)\cos(2ax+ah)$$
and $\lim_{y\to0}\dfrac{\sin y}y=1$
Here $a=1$
Similarly for $\cos$ if required
