derivative g(t)=t^2-2/(t^3)

解

導関数

g (t) = t^{2} - \frac{2}{t ^{3}}

2 t + \frac{6}{t ^{4}}

解答ステップ

\frac{d}{d t} (t^{2} - \frac{2}{t ^{3}})

和/差の法則を適用:

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

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

\frac{d}{d t} (t^{2}) = 2 t

\frac{d}{d t} (\frac{2}{t ^{3}}) = - \frac{6}{t ^{4}}

= 2 t - (- \frac{6}{t ^{4}})

簡素化

= 2 t + \frac{6}{t ^{4}}