derivative f(x)= x/((x-1)^2)

解答

导数

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

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

求解步骤

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

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

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

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

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

化简

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

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

\frac{d}{d t} (ln (2 t))

\int_{0}^{1} \frac{1}{x ^{3}} d x

\int \frac{9 t - 5}{t + 1} d t

x \to 0 lim (\frac{x - 32}{x - 4})

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