derivative f(x)= x/(x^2-x)

解答

导数

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

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

求解步骤

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

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

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

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

化简

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

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

\int (x^{3} - 6 x - 9) d x

d er i v a t i v e f (x) = \frac{4 x}{( x - 9 ) ^{5}}

t a y l or ln (4 x), 1

\int \frac{2 - x}{2 + x} d x

\frac{\partial}{\partial x} (x y - x sin (y))