derivative ((x-1))/(x^2+3)

解答

导数

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

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

求解步骤

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

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

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

\frac{d}{d x} (x^{2} + 3) = 2 x

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

化简

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

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

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