Question

Se $y= ln(cos(2x))$, então qual é o valor de $y' ( \frac{ \pi}{2} )$?

Answer 1

Olá, vamos derivar.

$\displaystyle y = \ln (\cos 2x) \\ \\ \\ y' = \frac{1}{\cos 2x} \cdot \cos 2x' \\ \\ \\ y' = \frac{1}{\cos 2x} \cdot - \sin 2x \cdot 2 \\ \\ \\ y' = -\frac{2 \sin 2x}{\cos 2x} \\ \\ \\ y'(\frac{\pi}{2}) = -\frac{2 \sin 2 \cdot \frac{\pi}{2}}{\cos 2 \cdot \frac{\pi}{2}} \\ \\ \\ y'(\frac{\pi}{2}) = 0$