derivative of (x^2(2/(x^2)+5/(x^3)))

解

\frac{d}{d x} ((x^{2}) (\frac{2}{x ^{2}} + \frac{5}{x ^{3}}))

- \frac{5}{x ^{2}}

解答ステップ

\frac{d}{d x} ((x^{2}) (\frac{2}{x ^{2}} + \frac{5}{x ^{3}}))

簡素化

(x^{2}) (\frac{2}{x ^{2}} + \frac{5}{x ^{3}}) : 2 + \frac{5}{x}

= \frac{d}{d x} (2 + \frac{5}{x})

和/差の法則を適用:

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

= \frac{d}{d x} (2) + \frac{d}{d x} (\frac{5}{x})

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

\frac{d}{d x} (\frac{5}{x}) = - \frac{5}{x ^{2}}

= 0 - \frac{5}{x ^{2}}

簡素化

= - \frac{5}{x ^{2}}