d/(dt)(((2t+1)^{3/2})/3)

解

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

(2 t + 1)^{\frac{1}{2}}

解答ステップ

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

定数を除去:

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

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

連鎖法則を適用:

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

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

\frac{d}{d t} (2 t + 1) = 2

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

簡素化

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

= (2 t + 1)^{\frac{1}{2}}