derivative ln((2x+3)/(3x-4))

解答

导数

ln (\frac{2 x + 3}{3 x - 4})

- \frac{17}{( 2 x + 3 ) ( 3 x - 4 )}

求解步骤

\frac{d}{d x} (ln (\frac{2 x + 3}{3 x - 4}))

使用连锁律:

\frac{1}{\frac{2 x + 3}{3 x - 4}} \frac{d}{d x} (\frac{2 x + 3}{3 x - 4})

= \frac{1}{\frac{2 x + 3}{3 x - 4}} \frac{d}{d x} (\frac{2 x + 3}{3 x - 4})

\frac{d}{d x} (\frac{2 x + 3}{3 x - 4}) = - \frac{17}{( 3 x - 4 ) ^{2}}

= \frac{1}{\frac{2 x + 3}{3 x - 4}} (- \frac{17}{( 3 x - 4 ) ^{2}})

化简

\frac{1}{\frac{2 x + 3}{3 x - 4}} (- \frac{17}{( 3 x - 4 ) ^{2}}) : - \frac{17}{( 2 x + 3 ) ( 3 x - 4 )}

= - \frac{17}{( 2 x + 3 ) ( 3 x - 4 )}

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