derivative (5x+6)(6x-7)

解

導関数

(5 x + 6) (6 x - 7)

60 x + 1

解答ステップ

\frac{d}{d x} ((5 x + 6) (6 x - 7))

積の法則を適用:

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

f = 5 x + 6, g = 6 x - 7

= \frac{d}{d x} (5 x + 6) (6 x - 7) + \frac{d}{d x} (6 x - 7) (5 x + 6)

\frac{d}{d x} (5 x + 6) = 5

\frac{d}{d x} (6 x - 7) = 6

= 5 (6 x - 7) + 6 (5 x + 6)

簡素化

5 (6 x - 7) + 6 (5 x + 6) : 60 x + 1

= 60 x + 1