derivative of ln(xcsch(7x))

解答

\frac{d}{d x} (ln (x) csch (7 x))

\frac{csch ( 7 x )}{x} - 7 coth (7 x) csch (7 x) ln (x)

求解步骤

\frac{d}{d x} (ln (x) csch (7 x))

使用微分乘法定则:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = ln (x), g = csch (7 x)

= \frac{d}{d x} (ln (x)) csch (7 x) + \frac{d}{d x} (csch (7 x)) ln (x)

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

\frac{d}{d x} (csch (7 x)) = - coth (7 x) csch (7 x) \cdot 7

= \frac{1}{x} csch (7 x) + (- coth (7 x) csch (7 x) \cdot 7) ln (x)

化简

\frac{1}{x} csch (7 x) + (- coth (7 x) csch (7 x) \cdot 7) ln (x) : \frac{csch ( 7 x )}{x} - 7 coth (7 x) csch (7 x) ln (x)

= \frac{csch ( 7 x )}{x} - 7 coth (7 x) csch (7 x) ln (x)

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