derivative f(x)=(3x-9)/(2x+8)

解答

导数

f (x) = \frac{3 x - 9}{2 x + 8}

\frac{21}{2 ( x + 4 ) ^{2}}

求解步骤

\frac{d}{d x} (\frac{3 x - 9}{2 x + 8})

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} ( 3 x - 9 ) ( 2 x + 8 ) - \frac{d}{d x} ( 2 x + 8 ) ( 3 x - 9 )}{( 2 x + 8 ) ^{2}}

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

\frac{d}{d x} (2 x + 8) = 2

= \frac{3 ( 2 x + 8 ) - 2 ( 3 x - 9 )}{( 2 x + 8 ) ^{2}}

化简

\frac{3 ( 2 x + 8 ) - 2 ( 3 x - 9 )}{( 2 x + 8 ) ^{2}} : \frac{21}{2 ( x + 4 ) ^{2}}

= \frac{21}{2 ( x + 4 ) ^{2}}

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