derivative ((-6x))/(sqrt(8-2x))

解答

导数

\frac{( - 6 x )}{8 - 2 x}

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

求解步骤

\frac{d}{d x} (\frac{- 6 x}{8 - 2 x})

化简

\frac{- 6 x}{8 - 2 x} : - \frac{6 x}{8 - 2 x}

= \frac{d}{d x} (- \frac{6 x}{8 - 2 x})

将常数提出:

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

= - 6 \frac{d}{d x} (\frac{x}{8 - 2 x})

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

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

\frac{d}{d x} (8 - 2 x) = - \frac{1}{8 - 2 x}

= - 6 \cdot \frac{1 \cdot 8 - 2 x - ( - \frac{1}{8 - 2 x} ) x}{( 8 - 2 x ) ^{2}}

化简

- 6 \cdot \frac{1 \cdot 8 - 2 x - ( - \frac{1}{8 - 2 x} ) x}{( 8 - 2 x ) ^{2}} : - \frac{3 ( - x + 8 )}{( - x + 4 ) - 2 x + 8}

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