derivative of-2/(cos(2x)+8/3)

解

\frac{d}{d x} (- \frac{2}{cos ( 2 x )} + \frac{8}{3})

- 4 sec (2 x) tan (2 x)

解答ステップ

\frac{d}{d x} (- \frac{2}{cos ( 2 x )} + \frac{8}{3})

簡素化

- \frac{2}{cos ( 2 x )} + \frac{8}{3} : - 2 sec (2 x) + \frac{8}{3}

= \frac{d}{d x} (- 2 sec (2 x) + \frac{8}{3})

和/差の法則を適用:

(f \pm g)^{'} = f^{'} \pm g^{'}

= - \frac{d}{d x} (2 sec (2 x)) + \frac{d}{d x} (\frac{8}{3})

\frac{d}{d x} (2 sec (2 x)) = 4 sec (2 x) tan (2 x)

\frac{d}{d x} (\frac{8}{3}) = 0

= - 4 sec (2 x) tan (2 x) + 0

簡素化

= - 4 sec (2 x) tan (2 x)