derivative v/(v-1)

解答

导数

\frac{v}{v - 1}

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

求解步骤

\frac{d}{d v} (\frac{v}{v - 1})

使用微分除法定则:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

\frac{d v}{d v} = 1

\frac{d}{d v} (v - 1) = 1

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

化简

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

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

x \to 0 lim (\frac{sin ( x )}{5 x})

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

\frac{d y}{d x} + 3 y = x

\int \frac{7}{x - 1} d x

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