derivative sqrt(t+t^3)

解

導関数

t + t^{3}

\frac{1 + 3 t ^{2}}{2 t + t ^{3}}

解答ステップ

\frac{d}{d t} (t + t^{3})

連鎖法則を適用:

\frac{1}{2 t + t ^{3}} \frac{d}{d t} (t + t^{3})

= \frac{1}{2 t + t ^{3}} \frac{d}{d t} (t + t^{3})

\frac{d}{d t} (t + t^{3}) = 1 + 3 t^{2}

= \frac{1}{2 t + t ^{3}} (1 + 3 t^{2})

簡素化

\frac{1}{2 t + t ^{3}} (1 + 3 t^{2}) : \frac{1 + 3 t ^{2}}{2 t + t ^{3}}

= \frac{1 + 3 t ^{2}}{2 t + t ^{3}}