derivative of-(200/(x^2))

解答

\frac{d}{d x} (- \frac{200}{x ^{2}})

\frac{400}{x ^{3}}

求解步骤

\frac{d}{d x} (- \frac{200}{x ^{2}})

将常数提出:

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

= - 200 \frac{d}{d x} (\frac{1}{x ^{2}})

使用指数法则:

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

= - 200 \frac{d}{d x} (x^{- 2})

使用幂法则:

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

= - 200 (- 2 x^{- 2 - 1})

化简

- 200 (- 2 x^{- 2 - 1}) : \frac{400}{x ^{3}}

= \frac{400}{x ^{3}}

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