(\partial)/(\partial x)(1/((x^2+y^2)))

解答

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

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

求解步骤

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

将

y

视为常数

使用指数法则:

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

= \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

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

化简

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

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

(x^{4} + y^{4}) d x - (x y^{3}) d y = 0

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2 r (s^{2} + 1) d r + (r^{4} + 1) d s = 0

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