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

解答

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

\frac{x ^{2} + 4 x - 12}{( 2 + x ) ^{2}}

求解步骤

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

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

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

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

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

化简

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

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

x \to 0 lim (\frac{1}{x ^{2} + x} - \frac{1}{x})

x \to - 5 lim (\frac{( x ^{2} + 6 x + 5 )}{x ^{2} + 4 x - 5})

y^{^{'}} = 3 y + 2

\int y (x + y) d y

\int \frac{1}{( 121 - x ^{2} ) ^{\frac{3}{2}}} d x