derivative f(x)= 1/x+1/(x^2)+1/(x^3)

解

導関数

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

- \frac{1}{x ^{2}} - \frac{2}{x ^{3}} - \frac{3}{x ^{4}}

解答ステップ

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

和/差の法則を適用:

(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 ^{3}})

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

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

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

= - \frac{1}{x ^{2}} - \frac{2}{x ^{3}} - \frac{3}{x ^{4}}