derivative of (-1-x/(x-1))

解答

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

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

求解步骤

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

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

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

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

化简

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

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

\int (x^{2} + 5)^{2} d x

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