derivative ((12x-7))/(3x-9)

解答

导数

\frac{( 12 x - 7 )}{3 x - 9}

- \frac{29}{3 ( x - 3 ) ^{2}}

求解步骤

\frac{d}{d x} (\frac{12 x - 7}{3 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} ( 12 x - 7 ) ( 3 x - 9 ) - \frac{d}{d x} ( 3 x - 9 ) ( 12 x - 7 )}{( 3 x - 9 ) ^{2}}

\frac{d}{d x} (12 x - 7) = 12

\frac{d}{d x} (3 x - 9) = 3

= \frac{12 ( 3 x - 9 ) - 3 ( 12 x - 7 )}{( 3 x - 9 ) ^{2}}

化简

\frac{12 ( 3 x - 9 ) - 3 ( 12 x - 7 )}{( 3 x - 9 ) ^{2}} : - \frac{29}{3 ( x - 3 ) ^{2}}

= - \frac{29}{3 ( x - 3 ) ^{2}}

f (x) = ln (3 x + 5)

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