derivative of (6x^2-6x+3(1+2x))

解

\frac{d}{d x} ((6 x^{2} - 6 x + 3) (1 + 2 x))

36 x^{2} - 12 x

解答ステップ

\frac{d}{d x} ((6 x^{2} - 6 x + 3) (1 + 2 x))

積の法則を適用:

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

f = 6 x^{2} - 6 x + 3, g = 1 + 2 x

= \frac{d}{d x} (6 x^{2} - 6 x + 3) (1 + 2 x) + \frac{d}{d x} (1 + 2 x) (6 x^{2} - 6 x + 3)

\frac{d}{d x} (6 x^{2} - 6 x + 3) = 12 x - 6

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

= (12 x - 6) (1 + 2 x) + 2 (6 x^{2} - 6 x + 3)

簡素化

(12 x - 6) (1 + 2 x) + 2 (6 x^{2} - 6 x + 3) : 36 x^{2} - 12 x

= 36 x^{2} - 12 x