derivative f(x)=4(x^2+4x)^3

解

導関数

f (x) = 4 (x^{2} + 4 x)^{3}

12 (x^{2} + 4 x)^{2} (2 x + 4)

解答ステップ

\frac{d}{d x} (4 (x^{2} + 4 x)^{3})

定数を除去:

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

= 4 \frac{d}{d x} ((x^{2} + 4 x)^{3})

連鎖法則を適用:

3 (x^{2} + 4 x)^{2} \frac{d}{d x} (x^{2} + 4 x)

= 3 (x^{2} + 4 x)^{2} \frac{d}{d x} (x^{2} + 4 x)

\frac{d}{d x} (x^{2} + 4 x) = 2 x + 4

= 4 \cdot 3 (x^{2} + 4 x)^{2} (2 x + 4)

簡素化

= 12 (x^{2} + 4 x)^{2} (2 x + 4)