derivative of 1/(sqrt(4-x))

解

\frac{d}{d x} (\frac{1}{4 - x})

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

解答ステップ

\frac{d}{d x} (\frac{1}{4 - x})

指数の規則を適用する:

\frac{1}{a} = a^{- 1}

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

連鎖法則を適用:

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

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

\frac{d}{d x} (4 - x) = - 1

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

簡素化

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