derivative y=(3x+4)/(sqrt(2x-1))

解答

导数

y = \frac{3 x + 4}{2 x - 1}

\frac{3 x - 7}{( 2 x - 1 ) 2 x - 1}

求解步骤

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

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

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

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

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

化简

\frac{3 2 x - 1 - \frac{1}{2 x - 1} ( 3 x + 4 )}{( 2 x - 1 ) ^{2}} : \frac{3 x - 7}{( 2 x - 1 ) 2 x - 1}

= \frac{3 x - 7}{( 2 x - 1 ) 2 x - 1}

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