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

解

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

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

解答ステップ

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

和/差の法則を適用:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

\frac{d}{d x} (1) = 0

= \frac{2}{3 ( x + 1 ) ^{\frac{1}{3}}} - \frac{2}{3 x ^{\frac{1}{3}}} + 0

簡素化

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