derivative g(x)=2x^{0.8}+4x^{-0.8}

解

導関数

g (x) = 2 x^{0.8} + 4 x^{- 0.8}

\frac{1.6}{x ^{0.2}} - \frac{3.2}{x ^{1.8}}

解答ステップ

\frac{d}{d x} (2 x^{0.8} + 4 x^{- 0.8})

和/差の法則を適用:

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

= \frac{d}{d x} (2 x^{0.8}) + \frac{d}{d x} (4 x^{- 0.8})

\frac{d}{d x} (2 x^{0.8}) = \frac{1.6}{x ^{0.2}}

\frac{d}{d x} (4 x^{- 0.8}) = - \frac{3.2}{x ^{1.8}}

= \frac{1.6}{x ^{0.2}} - \frac{3.2}{x ^{1.8}}