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

解

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

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

解答ステップ

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

連鎖法則を適用:

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

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

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

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

簡素化

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