derivative \sqrt[3]{(t^3-3)}

解

導関数

3 (t^{3} - 3)

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

解答ステップ

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

連鎖法則を適用:

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

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

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

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

簡素化

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

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