derivative f(x)=4-(20)/(x^3)+3/(x^5)

解

導関数

f (x) = 4 - \frac{20}{x ^{3}} + \frac{3}{x ^{5}}

\frac{60}{x ^{4}} - \frac{15}{x ^{6}}

解答ステップ

\frac{d}{d x} (4 - \frac{20}{x ^{3}} + \frac{3}{x ^{5}})

和/差の法則を適用:

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

= \frac{d}{d x} (4) - \frac{d}{d x} (\frac{20}{x ^{3}}) + \frac{d}{d x} (\frac{3}{x ^{5}})

\frac{d}{d x} (4) = 0

\frac{d}{d x} (\frac{20}{x ^{3}}) = - \frac{60}{x ^{4}}

\frac{d}{d x} (\frac{3}{x ^{5}}) = - \frac{15}{x ^{6}}

= 0 - (- \frac{60}{x ^{4}}) - \frac{15}{x ^{6}}

簡素化

= \frac{60}{x ^{4}} - \frac{15}{x ^{6}}