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

解答

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

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

求解步骤

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

将

x

视为常数

将常数提出:

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

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

使用指数法则:

\frac{1}{a} = a^{- 1}

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

使用连锁律:

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

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

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

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

化简

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

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

\frac{d}{d x} (sin^{3} (cos (x)))

\frac{d ^{2} y}{d x ^{2}} = \frac{( 6 x ^{5} )}{5} - 3 x

d er i v a t i v e y = \frac{x ^{2} + 1}{x + 1}

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

x \to 0 lim (\frac{4}{3 + e ^{\frac{1}{x}}})