derivative (0.4x+2)(0.5x-5)

解

導関数

(0.4 x + 2) (0.5 x - 5)

0.4 x - 1

解答ステップ

\frac{d}{d x} ((0.4 x + 2) (0.5 x - 5))

積の法則を適用:

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

f = 0.4 x + 2, g = 0.5 x - 5

= \frac{d}{d x} (0.4 x + 2) (0.5 x - 5) + \frac{d}{d x} (0.5 x - 5) (0.4 x + 2)

\frac{d}{d x} (0.4 x + 2) = 0.4

\frac{d}{d x} (0.5 x - 5) = 0.5

= 0.4 (0.5 x - 5) + 0.5 (0.4 x + 2)

簡素化

0.4 (0.5 x - 5) + 0.5 (0.4 x + 2) : 0.4 x - 1

= 0.4 x - 1