derivative of \sqrt[3]{x^2+6}

解

\frac{d}{d x} (3 x^{2} + 6)

\frac{2 x}{3 ( x ^{2} + 6 ) ^{\frac{2}{3}}}

解答ステップ

\frac{d}{d x} (3 x^{2} + 6)

連鎖法則を適用:

\frac{1}{3 ( x ^{2} + 6 ) ^{\frac{2}{3}}} \frac{d}{d x} (x^{2} + 6)

= \frac{1}{3 ( x ^{2} + 6 ) ^{\frac{2}{3}}} \frac{d}{d x} (x^{2} + 6)

\frac{d}{d x} (x^{2} + 6) = 2 x

= \frac{1}{3 ( x ^{2} + 6 ) ^{\frac{2}{3}}} \cdot 2 x

簡素化

\frac{1}{3 ( x ^{2} + 6 ) ^{\frac{2}{3}}} \cdot 2 x : \frac{2 x}{3 ( x ^{2} + 6 ) ^{\frac{2}{3}}}

= \frac{2 x}{3 ( x ^{2} + 6 ) ^{\frac{2}{3}}}