derivative f(x)=(x-5)(x+1)

解

導関数

f (x) = (x - 5) (x + 1)

2 x - 4

解答ステップ

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

積の法則を適用:

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

f = x - 5, g = x + 1

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

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

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

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

簡素化

1 \cdot (x + 1) + 1 \cdot (x - 5) : 2 x - 4

= 2 x - 4