derivative x^2(3-x)

解

導関数

x^{2} (3 - x)

6 x - 3 x^{2}

解答ステップ

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

積の法則を適用:

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

f = x^{2}, g = 3 - x

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

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

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

= 2 x (3 - x) + (- 1) x^{2}

簡素化

2 x (3 - x) + (- 1) x^{2} : 6 x - 3 x^{2}

= 6 x - 3 x^{2}