derivative of \sqrt[3]{-3x^2+5x+1}

解

\frac{d}{d x} (3 - 3 x^{2} + 5 x + 1)

\frac{- 6 x + 5}{3 ( - 3 x ^{2} + 5 x + 1 ) ^{\frac{2}{3}}}

解答ステップ

\frac{d}{d x} (3 - 3 x^{2} + 5 x + 1)

連鎖法則を適用:

\frac{1}{3 ( - 3 x ^{2} + 5 x + 1 ) ^{\frac{2}{3}}} \frac{d}{d x} (- 3 x^{2} + 5 x + 1)

= \frac{1}{3 ( - 3 x ^{2} + 5 x + 1 ) ^{\frac{2}{3}}} \frac{d}{d x} (- 3 x^{2} + 5 x + 1)

\frac{d}{d x} (- 3 x^{2} + 5 x + 1) = - 6 x + 5

= \frac{1}{3 ( - 3 x ^{2} + 5 x + 1 ) ^{\frac{2}{3}}} (- 6 x + 5)

簡素化

\frac{1}{3 ( - 3 x ^{2} + 5 x + 1 ) ^{\frac{2}{3}}} (- 6 x + 5) : \frac{- 6 x + 5}{3 ( - 3 x ^{2} + 5 x + 1 ) ^{\frac{2}{3}}}

= \frac{- 6 x + 5}{3 ( - 3 x ^{2} + 5 x + 1 ) ^{\frac{2}{3}}}