derivative of \sqrt[3]{(2-3x^2})

解

\frac{d}{d x} (3 (2 - 3 x)^{2})

- \frac{2}{( 2 - 3 x ) ^{\frac{1}{3}}}

解答ステップ

\frac{d}{d x} (3 (2 - 3 x)^{2})

連鎖法則を適用:

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

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

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

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

簡素化

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

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