derivative 1/2 x^2+2x-2+35x^{-1}

解答

导数

\frac{1}{2} x^{2} + 2 x - 2 + 35 x^{- 1}

x - \frac{35}{x ^{2}} + 2

求解步骤

\frac{d}{d x} (\frac{1}{2} x^{2} + 2 x - 2 + 35 x^{- 1})

使用微分加减法定则:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (\frac{1}{2} x^{2}) + \frac{d}{d x} (2 x) - \frac{d}{d x} (2) + \frac{d}{d x} (35 x^{- 1})

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

\frac{d}{d x} (2 x) = 2

\frac{d}{d x} (2) = 0

\frac{d}{d x} (35 x^{- 1}) = - \frac{35}{x ^{2}}

= x + 2 - 0 - \frac{35}{x ^{2}}

化简

= x - \frac{35}{x ^{2}} + 2

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