derivative of (x^2-9^{2/3})

解

\frac{d}{d x} ((x^{2} - 9)^{\frac{2}{3}})

\frac{4 x}{3 ( x ^{2} - 9 ) ^{\frac{1}{3}}}

解答ステップ

\frac{d}{d x} ((x^{2} - 9)^{\frac{2}{3}})

連鎖法則を適用:

\frac{2}{3 ( x ^{2} - 9 ) ^{\frac{1}{3}}} \frac{d}{d x} (x^{2} - 9)

= \frac{2}{3 ( x ^{2} - 9 ) ^{\frac{1}{3}}} \frac{d}{d x} (x^{2} - 9)

\frac{d}{d x} (x^{2} - 9) = 2 x

= \frac{2}{3 ( x ^{2} - 9 ) ^{\frac{1}{3}}} \cdot 2 x

簡素化

\frac{2}{3 ( x ^{2} - 9 ) ^{\frac{1}{3}}} \cdot 2 x : \frac{4 x}{3 ( x ^{2} - 9 ) ^{\frac{1}{3}}}

= \frac{4 x}{3 ( x ^{2} - 9 ) ^{\frac{1}{3}}}