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

解答

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

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

求解步骤

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

将

y

视为常数

将常数提出:

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

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

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

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

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

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

化简

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

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

in v erse l a pl a ce \frac{( s + 2 )}{( s + 1 ) ^{2}}

\frac{\partial}{\partial z} (x yz + x y^{5} + y z^{5} + z x^{5})

f (x) = 2 e^{3 x}

l a pl a ce t r an s f or m - 4 e^{4 t}

\frac{\partial}{\partial y} (cos (x))