derivative 2x(x+3)^2

解

導関数

2 x (x + 3)^{2}

2 (3 x^{2} + 12 x + 9)

解答ステップ

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

定数を除去:

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

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

積の法則を適用:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = (x + 3)^{2}

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

\frac{d x}{d x} = 1

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

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

簡素化

2 (1 \cdot (x + 3)^{2} + 2 (x + 3) x) : 2 (3 x^{2} + 12 x + 9)

= 2 (3 x^{2} + 12 x + 9)