(\partial)/(\partial x)((z(x+y))/(x+y+z))

解答

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

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

求解步骤

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

将

z, y

视为常数

将常数提出:

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

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

使用微分除法定则:

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

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

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

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

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

化简

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

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

x^{^{'}} = - 2 x

x \to - 10 lim (- (\frac{1}{x + 10}))

\int_{0}^{x} x^{2} + x^{4} d x

\frac{d}{d x} (a x^{2} e^{3 x})

\int 2 cos (x) cos (2 x) d x