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

解答

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

- \frac{1}{x ^{2}} - \frac{2}{x ^{3}}

求解步骤

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

使用微分加减法定则:

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

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

\frac{d}{d x} (1) = 0

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

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

= 0 - \frac{1}{x ^{2}} - \frac{2}{x ^{3}}

化简

= - \frac{1}{x ^{2}} - \frac{2}{x ^{3}}

\int x^{2} + k x + 1 d x

t an g e n t 12 (x - \frac{1}{x})^{4}, at x = 2

\frac{d}{d x} (5 + 4 x - x^{3})

a re a x^{2} - 1, - 1, 6

d er i v a t i v e y = (5 x^{4} - 3 x^{3}) (3 x^{2} - 7 x^{3})