derivative of (7-3x(x+5))

解

\frac{d}{d x} ((7 - 3 x) (x + 5))

- 6 x - 8

解答ステップ

\frac{d}{d x} ((7 - 3 x) (x + 5))

積の法則を適用:

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

f = 7 - 3 x, g = x + 5

= \frac{d}{d x} (7 - 3 x) (x + 5) + \frac{d}{d x} (x + 5) (7 - 3 x)

\frac{d}{d x} (7 - 3 x) = - 3

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

= (- 3) (x + 5) + 1 \cdot (7 - 3 x)

簡素化

(- 3) (x + 5) + 1 \cdot (7 - 3 x) : - 6 x - 8

= - 6 x - 8