derivative of (x^2-2x-1^{2/3})

解

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

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

解答ステップ

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

連鎖法則を適用:

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

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

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

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

分数を乗じる:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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