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

解答

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

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

求解步骤

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

使用连锁律:

\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)

化简

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

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