derivative of-(2x/(4-x^2))

解答

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

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

求解步骤

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

将常数提出:

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

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

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

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

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

化简

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

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

\int_{7}^{9} (x^{2} + 2 x - 2) d x

\frac{d}{d x} ((3)^{x})

\int \frac{2 x + 1}{4 x ^{2} + 4 x + 7} d x

f (x) = 3 sin (x)

d er i v a t i v e F (r) = \frac{2}{r ^{3}}