derivative of (4x+2/((3-2x)^3))

解答

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

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

求解步骤

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

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

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

\frac{d}{d x} ((3 - 2 x)^{3}) = - 6 (3 - 2 x)^{2}

= \frac{4 ( 3 - 2 x ) ^{3} - ( - 6 ( 3 - 2 x ) ^{2} ) ( 4 x + 2 )}{( ( 3 - 2 x ) ^{3} ) ^{2}}

化简

\frac{4 ( 3 - 2 x ) ^{3} - ( - 6 ( 3 - 2 x ) ^{2} ) ( 4 x + 2 )}{( ( 3 - 2 x ) ^{3} ) ^{2}} : \frac{8 ( 2 x + 3 )}{( 3 - 2 x ) ^{4}}

= \frac{8 ( 2 x + 3 )}{( 3 - 2 x ) ^{4}}