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

解答

导数

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

\frac{- x ^{2} + 4 x - 8}{( x + 2 ) ^{2} ( x - 3 ) ^{2}}

求解步骤

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

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

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

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

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

化简

\frac{1 \cdot ( x + 2 ) ( x - 3 ) - ( 2 x - 1 ) ( x - 2 )}{( ( x + 2 ) ( x - 3 ) ) ^{2}} : \frac{- x ^{2} + 4 x - 8}{( x + 2 ) ^{2} ( x - 3 ) ^{2}}

= \frac{- x ^{2} + 4 x - 8}{( x + 2 ) ^{2} ( x - 3 ) ^{2}}

y^{^{'}} = \frac{2 y}{x}, y (\frac{1}{2}) = 5

x \to 0 lim (\frac{( x ^{3} )}{x})

\int_{- 1}^{3} x d x

\int (2 x^{3} + 5 x^{2} - 2 x + 1) d x

d er i v a t i v e x (x + 1)^{- 1}