derivative 4/3 pi(3+x)^3

解

導関数

\frac{4}{3} π (3 + x)^{3}

4 π (3 + x)^{2}

解答ステップ

\frac{d}{d x} (\frac{4}{3} π (3 + x)^{3})

定数を除去:

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

= \frac{4}{3} π \frac{d}{d x} ((3 + x)^{3})

連鎖法則を適用:

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

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

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

= \frac{4}{3} π 3 (3 + x)^{2} \cdot 1

簡素化

\frac{4}{3} π 3 (3 + x)^{2} \cdot 1 : 4 π (3 + x)^{2}

= 4 π (3 + x)^{2}