(\partial}{\partial x}(\frac{3y^2)/x)

解答

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

- \frac{3 y ^{2}}{x ^{2}}

求解步骤

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

将

y

视为常数

将常数提出:

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

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

使用指数法则:

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

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

使用幂法则:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

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

化简

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

= - \frac{3 y ^{2}}{x ^{2}}

\int (3 x^{5} - x^{3} + 6) d x

\int_{0}^{8} \frac{x}{4} d x

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