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

解答

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

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

求解步骤

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

使用指数法则:

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

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

使用连锁律:

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

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

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

= x (- \frac{2}{( x + y ) ^{3}} \cdot 1)

化简

x (- \frac{2}{( x + y ) ^{3}} \cdot 1) : - \frac{2 x}{( x + y ) ^{3}}

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

\int_{1}^{3} (x^{3} + \frac{1}{4 x ^{3}}) d x

n or ma l y = 2 x - 1 + 4 x^{2}, (1, 5)

\int k e^{- x} d x

\frac{\partial}{\partial x} (y (e^{x} + x e^{x}))

d er i v a t i v e g (x) = \frac{1}{4 x ^{2} + 2 x}