derivative of 1-x^{2/3}

解答

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

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

求解步骤

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

使用微分加减法定则:

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

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

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

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

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

化简

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