(\partial)/(\partial y)(((-y^2))/((x-y)^2))

解答

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

- \frac{2 y x}{( x - y ) ^{3}}

求解步骤

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

化简

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

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

将

x

视为常数

将常数提出:

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

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

使用微分除法定则:

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

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

\frac{\partial}{\partial y} (y^{2}) = 2 y

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

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

化简

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

= - \frac{2 y x}{( x - y ) ^{3}}

x \to 5 - lim (\frac{2}{x})

x \to 2 lim (\frac{x ^{2} + 6 x - 2 x}{x - 2})

\frac{1}{x ^{5}} \frac{d y}{d x} = 2 + 18 y

d er i v a t i v e cos^{8} (x)

\frac{\partial}{\partial x} (5 y cos (x))