derivative of (2x-1(3x+5))

解

\frac{d}{d x} ((2 x - 1) (3 x + 5))

12 x + 7

解答ステップ

\frac{d}{d x} ((2 x - 1) (3 x + 5))

積の法則を適用:

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

f = 2 x - 1, g = 3 x + 5

= \frac{d}{d x} (2 x - 1) (3 x + 5) + \frac{d}{d x} (3 x + 5) (2 x - 1)

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

\frac{d}{d x} (3 x + 5) = 3

= 2 (3 x + 5) + 3 (2 x - 1)

簡素化

2 (3 x + 5) + 3 (2 x - 1) : 12 x + 7

= 12 x + 7