derivative f(x)=36x^{-2}-2x^{-4}+2

解

導関数

f (x) = 36 x^{- 2} - 2 x^{- 4} + 2

\frac{8}{x ^{5}} - \frac{72}{x ^{3}}

解答ステップ

\frac{d}{d x} (36 x^{- 2} - 2 x^{- 4} + 2)

和/差の法則を適用:

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

= \frac{d}{d x} (36 x^{- 2}) - \frac{d}{d x} (2 x^{- 4}) + \frac{d}{d x} (2)

\frac{d}{d x} (36 x^{- 2}) = - \frac{72}{x ^{3}}

\frac{d}{d x} (2 x^{- 4}) = - \frac{8}{x ^{5}}

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

= - \frac{72}{x ^{3}} - (- \frac{8}{x ^{5}}) + 0

簡素化

= \frac{8}{x ^{5}} - \frac{72}{x ^{3}}