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

解

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

12 x + 20

解答ステップ

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

積の法則を適用:

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

f = 3 x + 1, g = 2 x + 6

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

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

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

= 3 (2 x + 6) + 2 (3 x + 1)

簡素化

3 (2 x + 6) + 2 (3 x + 1) : 12 x + 20

= 12 x + 20