derivative of (-12x/((x^2+3)^2))

解答

\frac{d}{d x} (\frac{- 12 x}{( x ^{2} + 3 ) ^{2}})

- \frac{36 ( - x ^{2} + 1 )}{( x ^{2} + 3 ) ^{3}}

求解步骤

\frac{d}{d x} (\frac{- 12 x}{( x ^{2} + 3 ) ^{2}})

化简

\frac{- 12 x}{( x ^{2} + 3 ) ^{2}} : - \frac{12 x}{( x ^{2} + 3 ) ^{2}}

= \frac{d}{d x} (- \frac{12 x}{( x ^{2} + 3 ) ^{2}})

将常数提出:

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

= - 12 \frac{d}{d x} (\frac{x}{( x ^{2} + 3 ) ^{2}})

使用微分除法定则:

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

= - 12 \cdot \frac{\frac{d x}{d x} ( x ^{2} + 3 ) ^{2} - \frac{d}{d x} ( ( x ^{2} + 3 ) ^{2} ) x}{( ( x ^{2} + 3 ) ^{2} ) ^{2}}

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

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

= - 12 \cdot \frac{1 \cdot ( x ^{2} + 3 ) ^{2} - 4 x ( x ^{2} + 3 ) x}{( ( x ^{2} + 3 ) ^{2} ) ^{2}}

化简

- 12 \cdot \frac{1 \cdot ( x ^{2} + 3 ) ^{2} - 4 x ( x ^{2} + 3 ) x}{( ( x ^{2} + 3 ) ^{2} ) ^{2}} : - \frac{36 ( - x ^{2} + 1 )}{( x ^{2} + 3 ) ^{3}}

= - \frac{36 ( - x ^{2} + 1 )}{( x ^{2} + 3 ) ^{3}}

d er i v a t i v e 2 x^{2} - 6 x + 3

\int_{2}^{3} \frac{27}{3 - x} d x

n = 2 \sum \infty e^{3 - 6 n}

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

\int_{- 2}^{2} \frac{10}{x ^{2} - 2 x - 24} d x