Ҳосилаи функсияи \(f(x) = \cos 2x - 2\sin x\) ёфта шавад.

Ҳал.

\(\begin{multline}
f'(x) = \left(\cos 2x - 2\sin x\right)' = \left(\cos 2x\right)' - 2\left(\sin x\right)' = -\sin 2x\cdot (2x)' - 2\cos x = \\
= -2\sin 2x - 2\cos x = -2\cdot 2\cdot \sin x\cdot \cos x - 2\cos x = - 2\cos x(2\sin x + 1).
\end{multline}\)

Ҷавоб.

\[f'(x) = - 2\cos x(1 + 2\sin x).\]