derivative of 1/6 (2x+1^3)

解

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

(2 x + 1)^{2}

解答ステップ

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

定数を除去:

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

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

連鎖法則を適用:

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

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

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

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

簡素化

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

= (2 x + 1)^{2}