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

解答

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

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

求解步骤

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

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

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

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

化简

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

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

\frac{( x ^{2} + 1 ) d y}{d x} + 8 x (y - 1) = 0

\int \frac{x + 4}{x} d x

d er i v a t i v e f (x) = tan (\frac{π}{3})

\frac{d}{d x} (\frac{e ^{i x} + e ^{- i x}}{2})