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

解答

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

- \frac{4 x ( - x ^{2} + 3 )}{( x ^{2} + 1 ) ^{3}}

求解步骤

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

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

\frac{d}{d x} (- 2 x^{2} + 2) = - 4 x

\frac{d}{d x} ((x^{2} + 1)^{2}) = 4 x (x^{2} + 1)

= \frac{( - 4 x ) ( x ^{2} + 1 ) ^{2} - 4 x ( x ^{2} + 1 ) ( - 2 x ^{2} + 2 )}{( ( x ^{2} + 1 ) ^{2} ) ^{2}}

化简

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

= - \frac{4 x ( - x ^{2} + 3 )}{( x ^{2} + 1 ) ^{3}}

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

\int \frac{x ^{4} + 3 x + 3 x}{5 x ^{3}} d x

\frac{d}{d x} (- 8 ln (x))

d er i v a t i v e y = 7 x^{- 7}

(3 x + 2 y + 2 y^{2}) d x + (x + 2 x y) d y = 0