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

解

導関数

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

3 x^{2} + 12 x + 9

解答ステップ

\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}

= \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)

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

簡素化

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

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