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

解答

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

\frac{4 y}{( 3 + 2 x ) ^{2}}

求解步骤

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

将

y

视为常数

将常数提出:

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

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

使用指数法则:

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

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

使用连锁律:

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

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

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

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

化简

- 2 y (- \frac{1}{( 3 + 2 x ) ^{2}} \cdot 2) : \frac{4 y}{( 3 + 2 x ) ^{2}}

= \frac{4 y}{( 3 + 2 x ) ^{2}}

\int \frac{- 28}{x ^{2} x ^{2} + 25} d x

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