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

解答

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

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

求解步骤

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

将常数提出:

(a \cdot f)^{'} = a \cdot f^{'}

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

使用微分除法定则:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

\frac{d x}{d x} = 1

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

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

化简

- 2 \cdot \frac{1 \cdot ( - 3 + x ^{2} ) ^{2} - 4 x ( - 3 + x ^{2} ) x}{( ( - 3 + x ^{2} ) ^{2} ) ^{2}} : \frac{6 ( x ^{2} + 1 )}{( x ^{2} - 3 ) ^{3}}

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

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

\int_{b}^{a} f (x) d x

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

x \to 0 lim (e^{x^{2}})

\int_{1}^{2} x^{3} ln (x) d x