derivative of 7arctanh(cos(x))

解

\frac{d}{d x} (7 arctanh (cos (x)))

- 7 csc (x)

解答ステップ

\frac{d}{d x} (7 arctanh (cos (x)))

定数を除去:

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

= 7 \frac{d}{d x} (arctanh (cos (x)))

連鎖法則を適用:

\frac{1}{1 - ( cos ( x ) ) ^{2}} \frac{d}{d x} (cos (x))

= \frac{1}{1 - ( cos ( x ) ) ^{2}} \frac{d}{d x} (cos (x))

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

= 7 \cdot \frac{1}{1 - ( cos ( x ) ) ^{2}} (- sin (x))

簡素化

7 \cdot \frac{1}{1 - cos ^{2} ( x )} (- sin (x)) : - 7 csc (x)

= - 7 csc (x)