derivative y=(3x^2+2)(4x-1)

解

導関数

y = (3 x^{2} + 2) (4 x - 1)

36 x^{2} - 6 x + 8

解答ステップ

\frac{d}{d x} ((3 x^{2} + 2) (4 x - 1))

積の法則を適用:

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

f = 3 x^{2} + 2, g = 4 x - 1

= \frac{d}{d x} (3 x^{2} + 2) (4 x - 1) + \frac{d}{d x} (4 x - 1) (3 x^{2} + 2)

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

\frac{d}{d x} (4 x - 1) = 4

= 6 x (4 x - 1) + 4 (3 x^{2} + 2)

簡素化

6 x (4 x - 1) + 4 (3 x^{2} + 2) : 36 x^{2} - 6 x + 8

= 36 x^{2} - 6 x + 8