derivative g(x)=(x^2+3)(x^2-4x)

解

導関数

g (x) = (x^{2} + 3) (x^{2} - 4 x)

4 x^{3} - 12 x^{2} + 6 x - 12

解答ステップ

\frac{d}{d x} ((x^{2} + 3) (x^{2} - 4 x))

積の法則を適用:

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

f = x^{2} + 3, g = x^{2} - 4 x

= \frac{d}{d x} (x^{2} + 3) (x^{2} - 4 x) + \frac{d}{d x} (x^{2} - 4 x) (x^{2} + 3)

\frac{d}{d x} (x^{2} + 3) = 2 x

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

= 2 x (x^{2} - 4 x) + (2 x - 4) (x^{2} + 3)

簡素化

2 x (x^{2} - 4 x) + (2 x - 4) (x^{2} + 3) : 4 x^{3} - 12 x^{2} + 6 x - 12

= 4 x^{3} - 12 x^{2} + 6 x - 12