(\partial)/(\partial x)(-1/x)

解答

\frac{\partial}{\partial x} (- \frac{1}{x})

\frac{1}{x ^{2}}

求解步骤

\frac{\partial}{\partial x} (- \frac{1}{x})

将常数提出:

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

= - \frac{\partial}{\partial x} (\frac{1}{x})

使用指数法则:

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

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

使用幂法则:

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

= - (- 1 \cdot x^{- 1 - 1})

化简

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

= \frac{1}{x ^{2}}

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