derivative \sqrt[3]{6x^2+1}

解

導関数

3 6 x^{2} + 1

\frac{4 x}{( 6 x ^{2} + 1 ) ^{\frac{2}{3}}}

解答ステップ

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

連鎖法則を適用:

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

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

\frac{d}{d x} (6 x^{2} + 1) = 12 x

= \frac{1}{3 ( 6 x ^{2} + 1 ) ^{\frac{2}{3}}} \cdot 12 x

簡素化

\frac{1}{3 ( 6 x ^{2} + 1 ) ^{\frac{2}{3}}} \cdot 12 x : \frac{4 x}{( 6 x ^{2} + 1 ) ^{\frac{2}{3}}}

= \frac{4 x}{( 6 x ^{2} + 1 ) ^{\frac{2}{3}}}