derivative of ln(coth(x))

解

\frac{d}{d x} (ln (coth (x)))

- csch^{2} (x) tanh (x)

解答ステップ

\frac{d}{d x} (ln (coth (x)))

連鎖法則を適用:

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

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

\frac{d}{d x} (coth (x)) = - csch^{2} (x)

= \frac{1}{coth ( x )} (- csch^{2} (x))

簡素化

\frac{1}{coth ( x )} (- csch^{2} (x)) : - csch^{2} (x) tanh (x)

= - csch^{2} (x) tanh (x)