derivative y=4ln(cos(x))

解

導関数

y = 4 ln (cos (x))

- 4 tan (x)

解答ステップ

\frac{d}{d x} (4 ln (cos (x)))

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

= 4 \frac{d}{d x} (ln (cos (x)))

連鎖法則を適用:

\frac{1}{cos ( x )} \frac{d}{d x} (cos (x))

= \frac{1}{cos ( x )} \frac{d}{d x} (cos (x))

\frac{d}{d x} (cos (x)) = - sin (x)

= 4 \cdot \frac{1}{cos ( x )} (- sin (x))

簡素化

4 \cdot \frac{1}{cos ( x )} (- sin (x)) : - 4 tan (x)

= - 4 tan (x)