Answer
At $x=0$, $r'=2$
Work Step by Step
We have $\frac{dr}{dt}=\sin(f(t))$, $f(0)=\pi/3$ and $f'(0)=4$.
According to the Chain Rule: $$r'=(\sin(f(t)))'\times (f(t))'$$
At $x=0$: $$r'(0)=(\sin(f(0)))'\times f'(0)$$
We have $f(0)=\pi/3$ and $f'(0)=4$: $$r'(0)=\cos\Big(\frac{\pi}{3}\Big)\times4=\frac{1}{2}*4=2$$
