derivative of (-6x/(sqrt(2x-1)))

解答

\frac{d}{d x} (\frac{- 6 x}{2 x - 1})

- \frac{6 ( x - 1 )}{( 2 x - 1 ) 2 x - 1}

求解步骤

\frac{d}{d x} (\frac{- 6 x}{2 x - 1})

化简

\frac{- 6 x}{2 x - 1} : - \frac{6 x}{2 x - 1}

= \frac{d}{d x} (- \frac{6 x}{2 x - 1})

将常数提出:

(a \cdot f)^{'} = a \cdot f^{'}

= - 6 \frac{d}{d x} (\frac{x}{2 x - 1})

使用微分除法定则:

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

= - 6 \cdot \frac{\frac{d x}{d x} 2 x - 1 - \frac{d}{d x} ( 2 x - 1 ) x}{( 2 x - 1 ) ^{2}}

\frac{d x}{d x} = 1

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

= - 6 \cdot \frac{1 \cdot 2 x - 1 - \frac{1}{2 x - 1} x}{( 2 x - 1 ) ^{2}}

化简

- 6 \cdot \frac{1 \cdot 2 x - 1 - \frac{1}{2 x - 1} x}{( 2 x - 1 ) ^{2}} : - \frac{6 ( x - 1 )}{( 2 x - 1 ) 2 x - 1}

= - \frac{6 ( x - 1 )}{( 2 x - 1 ) 2 x - 1}

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