derivative of (5x-7/(6x-9))

解答

\frac{d}{d x} (\frac{5 x - 7}{6 x - 9})

- \frac{1}{3 ( 2 x - 3 ) ^{2}}

求解步骤

\frac{d}{d x} (\frac{5 x - 7}{6 x - 9})

使用微分除法定则:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( 5 x - 7 ) ( 6 x - 9 ) - \frac{d}{d x} ( 6 x - 9 ) ( 5 x - 7 )}{( 6 x - 9 ) ^{2}}

\frac{d}{d x} (5 x - 7) = 5

\frac{d}{d x} (6 x - 9) = 6

= \frac{5 ( 6 x - 9 ) - 6 ( 5 x - 7 )}{( 6 x - 9 ) ^{2}}

化简

\frac{5 ( 6 x - 9 ) - 6 ( 5 x - 7 )}{( 6 x - 9 ) ^{2}} : - \frac{1}{3 ( 2 x - 3 ) ^{2}}

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

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