derivative of x^{-2}*ln(x)

解答

\frac{d}{d x} (x^{- 2} \cdot ln (x))

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

求解步骤

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

使用微分乘法定则:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{- 2}, g = ln (x)

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

\frac{d}{d x} (x^{- 2}) = - \frac{2}{x ^{3}}

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

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

化简

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

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

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