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

解

導関数

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

3 x^{2} + 8 x - 4

解答ステップ

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

積の法則を適用:

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

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

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

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

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

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

簡素化

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

= 3 x^{2} + 8 x - 4