derivative (x+6)/(x^3+x-7)

解答

导数

\frac{x + 6}{x ^{3} + x - 7}

\frac{- 2 x ^{3} - 18 x ^{2} - 13}{( x ^{3} + x - 7 ) ^{2}}

求解步骤

\frac{d}{d x} (\frac{x + 6}{x ^{3} + x - 7})

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 + 6 ) ( x ^{3} + x - 7 ) - \frac{d}{d x} ( x ^{3} + x - 7 ) ( x + 6 )}{( x ^{3} + x - 7 ) ^{2}}

\frac{d}{d x} (x + 6) = 1

\frac{d}{d x} (x^{3} + x - 7) = 3 x^{2} + 1

= \frac{1 \cdot ( x ^{3} + x - 7 ) - ( 3 x ^{2} + 1 ) ( x + 6 )}{( x ^{3} + x - 7 ) ^{2}}

化简

\frac{1 \cdot ( x ^{3} + x - 7 ) - ( 3 x ^{2} + 1 ) ( x + 6 )}{( x ^{3} + x - 7 ) ^{2}} : \frac{- 2 x ^{3} - 18 x ^{2} - 13}{( x ^{3} + x - 7 ) ^{2}}

= \frac{- 2 x ^{3} - 18 x ^{2} - 13}{( x ^{3} + x - 7 ) ^{2}}

\int x (x + 4)^{6} d x

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