derivative x^2(1-6x)

解

導関数

x^{2} (1 - 6 x)

2 x - 18 x^{2}

解答ステップ

\frac{d}{d x} (x^{2} (1 - 6 x))

積の法則を適用:

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

f = x^{2}, g = 1 - 6 x

= \frac{d}{d x} (x^{2}) (1 - 6 x) + \frac{d}{d x} (1 - 6 x) x^{2}

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

\frac{d}{d x} (1 - 6 x) = - 6

= 2 x (1 - 6 x) + (- 6) x^{2}

簡素化

2 x (1 - 6 x) + (- 6) x^{2} : 2 x - 18 x^{2}

= 2 x - 18 x^{2}