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

解答

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

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

求解步骤

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

将

x

视为常数

使用指数法则:

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

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

使用连锁律:

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

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

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

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

化简

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

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

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