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

解答

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

- \frac{4 x}{( x ^{2} + y ^{2} ) ^{2}}

求解步骤

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

将

y

视为常数

将常数提出:

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

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

使用指数法则:

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

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

使用连锁律:

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

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

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

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

化简

2 (- \frac{1}{( x ^{2} + y ^{2} ) ^{2}} \cdot 2 x) : - \frac{4 x}{( x ^{2} + y ^{2} ) ^{2}}

= - \frac{4 x}{( x ^{2} + y ^{2} ) ^{2}}

(y^{3} - 1) e^{x} d x + 3 y^{2} (e^{x} + 1) d y = 0

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