derivative of 2x^2-1/(x^2+1/(x^3))

解答

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

4 x + \frac{2}{x ^{3}} - \frac{3}{x ^{4}}

求解步骤

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

使用微分加减法定则:

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

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

\frac{d}{d x} (2 x^{2}) = 4 x

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

\frac{d}{d x} (\frac{1}{x ^{3}}) = - \frac{3}{x ^{4}}

= 4 x - (- \frac{2}{x ^{3}}) - \frac{3}{x ^{4}}

化简

= 4 x + \frac{2}{x ^{3}} - \frac{3}{x ^{4}}

\int \frac{31}{x ^{3} - 27} d x

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