If $f(x) = \sin^{2} 2x$, what is $f'\left(\frac{\pi}{8}\right)$?

Explanation

1. 01

   $f'(x) = 2\sin 2x \cdot \cos 2x \cdot 2 = 2\sin 4x$.

2. 02

   At $\frac{\pi}{8}$: $2\sin \frac{\pi}{2} = 2$.