derivative of (x-7/(-5x-10))

解答

\frac{d}{d x} (\frac{x - 7}{- 5 x - 10})

- \frac{9}{5 ( x + 2 ) ^{2}}

求解步骤

\frac{d}{d x} (\frac{x - 7}{- 5 x - 10})

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} ( x - 7 ) ( - 5 x - 10 ) - \frac{d}{d x} ( - 5 x - 10 ) ( x - 7 )}{( - 5 x - 10 ) ^{2}}

\frac{d}{d x} (x - 7) = 1

\frac{d}{d x} (- 5 x - 10) = - 5

= \frac{1 \cdot ( - 5 x - 10 ) - ( - 5 ) ( x - 7 )}{( - 5 x - 10 ) ^{2}}

化简

\frac{1 \cdot ( - 5 x - 10 ) - ( - 5 ) ( x - 7 )}{( - 5 x - 10 ) ^{2}} : - \frac{9}{5 ( x + 2 ) ^{2}}

= - \frac{9}{5 ( x + 2 ) ^{2}}

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