derivative of 2/3 (x+3^{3/2})

解

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

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

解答ステップ

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

定数を除去:

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

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

連鎖法則を適用:

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

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

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

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

簡素化

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

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