derivative f(x)=(x-4)(x^2+8)

解

導関数

f (x) = (x - 4) (x^{2} + 8)

3 x^{2} - 8 x + 8

解答ステップ

\frac{d}{d x} ((x - 4) (x^{2} + 8))

積の法則を適用:

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

f = x - 4, g = x^{2} + 8

= \frac{d}{d x} (x - 4) (x^{2} + 8) + \frac{d}{d x} (x^{2} + 8) (x - 4)

\frac{d}{d x} (x - 4) = 1

\frac{d}{d x} (x^{2} + 8) = 2 x

= 1 \cdot (x^{2} + 8) + 2 x (x - 4)

簡素化

1 \cdot (x^{2} + 8) + 2 x (x - 4) : 3 x^{2} - 8 x + 8

= 3 x^{2} - 8 x + 8