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

解

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

- \frac{9}{( 6 x + 3 ) ^{\frac{3}{2}}}

解答ステップ

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

定数を除去:

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

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

指数の規則を適用する:

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

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

連鎖法則を適用:

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

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

\frac{d}{d x} (6 x + 3) = 6

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

簡素化

3 (- \frac{1}{2 ( 6 x + 3 ) ^{\frac{3}{2}}} \cdot 6) : - \frac{9}{( 6 x + 3 ) ^{\frac{3}{2}}}

= - \frac{9}{( 6 x + 3 ) ^{\frac{3}{2}}}