derivative of ln((5x+1/(5x-1)))

解答

\frac{d}{d x} (ln (\frac{5 x + 1}{5 x - 1}))

- \frac{10}{( 5 x + 1 ) ( 5 x - 1 )}

求解步骤

\frac{d}{d x} (ln (\frac{5 x + 1}{5 x - 1}))

使用连锁律:

\frac{1}{\frac{5 x + 1}{5 x - 1}} \frac{d}{d x} (\frac{5 x + 1}{5 x - 1})

= \frac{1}{\frac{5 x + 1}{5 x - 1}} \frac{d}{d x} (\frac{5 x + 1}{5 x - 1})

\frac{d}{d x} (\frac{5 x + 1}{5 x - 1}) = - \frac{10}{( 5 x - 1 ) ^{2}}

= \frac{1}{\frac{5 x + 1}{5 x - 1}} (- \frac{10}{( 5 x - 1 ) ^{2}})

化简

\frac{1}{\frac{5 x + 1}{5 x - 1}} (- \frac{10}{( 5 x - 1 ) ^{2}}) : - \frac{10}{( 5 x + 1 ) ( 5 x - 1 )}

= - \frac{10}{( 5 x + 1 ) ( 5 x - 1 )}

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