derivative (42)/x

解答

导数

\frac{42}{x}

- \frac{42}{x ^{2}}

求解步骤

\frac{d}{d x} (\frac{42}{x})

将常数提出:

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

= 42 \frac{d}{d x} (\frac{1}{x})

使用指数法则:

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

= 42 \frac{d}{d x} (x^{- 1})

使用幂法则:

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

= 42 (- 1 \cdot x^{- 1 - 1})

化简

42 (- 1 \cdot x^{- 1 - 1}) : - \frac{42}{x ^{2}}

= - \frac{42}{x ^{2}}

x \to - 2 lim (3 x + 8)

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