derivative of ln(tanh(x))

解答

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

sech^{2} (x) coth (x)

求解步骤

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

使用连锁律:

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

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

\frac{d}{d x} (tanh (x)) = sech^{2} (x)

= \frac{1}{tanh ( x )} sech^{2} (x)

化简

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

= sech^{2} (x) coth (x)

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