Cho \(f\left(x\right)=\sin^22x.\) Tính \(f'\left(\dfrac{\pi}{4}\right)+f"\left(\dfrac{\pi}{8}\right)\).
\(0\).\(2\).\(10\).\(-6\).Hướng dẫn giải:\(f\left(x\right)=\sin^22x=\dfrac{1-\cos4x}{2}\Rightarrow f'\left(x\right)=2\sin4x\Rightarrow f"\left(x\right)=8\cos4x\). Do đó \(f'\left(\dfrac{\pi}{4}\right)=2\sin\pi=0;f"\left(\dfrac{\pi}{8}\right)=8\cos\dfrac{\pi}{2}=0\) và \(f'\left(\dfrac{\pi}{4}\right)+f"\left(\dfrac{\pi}{8}\right)=0.\)
