derivative ((2-1/x))/(x-3)

解答

导数

\frac{( 2 - \frac{1}{x} )}{x - 3}

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

求解步骤

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

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

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

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

化简

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

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

\int \frac{27}{( 1 - x ^{2} ) ^{\frac{3}{2}}} d x

\frac{d}{d x} (cot (sin (x)))

\frac{d y}{d x} = e^{- k \cdot a \cdot x}, y (0) = 0

t an g e n t x^{3} - 3 x - 4

\frac{d}{d y} (\frac{2}{3} (y - 1)^{\frac{3}{2}})