(\partial)/(\partial x)((xy)/(1+x))

解答

\frac{\partial}{\partial x} (\frac{x y}{1 + x})

\frac{y}{( 1 + x ) ^{2}}

求解步骤

\frac{\partial}{\partial x} (\frac{x y}{1 + x})

将

y

视为常数

将常数提出:

(a \cdot f)^{'} = a \cdot f^{'}

= y \frac{\partial}{\partial x} (\frac{x}{1 + x})

使用微分除法定则:

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

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

\frac{\partial}{\partial x} (x) = 1

\frac{\partial}{\partial x} (1 + x) = 1

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

化简

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

= \frac{y}{( 1 + x ) ^{2}}

\int - cos (d) x d x

n = 0 \sum \infty \frac{1}{2 n + 4}

\int 28 x^{3} - 15 x^{2} + 10 x d x

in v erse l a pl a ce \frac{5}{2 ( s - e ) ^{2} + 50}

in v erse l a pl a ce \frac{25}{s ^{3} ( s ^{2} + 4 s + 5 )}