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受欢迎的微积分 >

(\partial)/(\partial y)((1+x^2)/(3y-y^2))

解答

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

解答

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

求解步骤

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

将

x

视为常数

将常数提出:

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

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

使用指数法则:

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

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

使用连锁律:

- \frac{1}{( 3 y - y ^{2} ) ^{2}} \frac{\partial}{\partial y} (3 y - y^{2})

= - \frac{1}{( 3 y - y ^{2} ) ^{2}} \frac{\partial}{\partial y} (3 y - y^{2})

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

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

化简

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

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

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