derivative 4(t^5)/5-(t^3)/6

解

導関数

4 \frac{t ^{5}}{5} - \frac{t ^{3}}{6}

4 t^{4} - \frac{t ^{2}}{2}

解答ステップ

\frac{d}{d t} (4 \cdot \frac{t ^{5}}{5} - \frac{t ^{3}}{6})

簡素化

4 \cdot \frac{t ^{5}}{5} - \frac{t ^{3}}{6} : \frac{4 t ^{5}}{5} - \frac{t ^{3}}{6}

= \frac{d}{d t} (\frac{4 t ^{5}}{5} - \frac{t ^{3}}{6})

和/差の法則を適用:

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

= \frac{d}{d t} (\frac{4 t ^{5}}{5}) - \frac{d}{d t} (\frac{t ^{3}}{6})

\frac{d}{d t} (\frac{4 t ^{5}}{5}) = 4 t^{4}

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

= 4 t^{4} - \frac{t ^{2}}{2}