derivative of 3/(sqrt(6-x))

解

\frac{d}{d x} (\frac{3}{6 - x})

\frac{3}{2 ( 6 - x ) ^{\frac{3}{2}}}

解答ステップ

\frac{d}{d x} (\frac{3}{6 - x})

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

= 3 \frac{d}{d x} (\frac{1}{6 - x})

指数の規則を適用する:

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

= 3 \frac{d}{d x} ((6 - x)^{- \frac{1}{2}})

連鎖法則を適用:

- \frac{1}{2 ( 6 - x ) ^{\frac{3}{2}}} \frac{d}{d x} (6 - x)

= - \frac{1}{2 ( 6 - x ) ^{\frac{3}{2}}} \frac{d}{d x} (6 - x)

\frac{d}{d x} (6 - x) = - 1

= 3 (- \frac{1}{2 ( 6 - x ) ^{\frac{3}{2}}} (- 1))

簡素化

3 (- \frac{1}{2 ( 6 - x ) ^{\frac{3}{2}}} (- 1)) : \frac{3}{2 ( 6 - x ) ^{\frac{3}{2}}}

= \frac{3}{2 ( 6 - x ) ^{\frac{3}{2}}}