derivative (x^2-2)(x^3-3x)

解

導関数

(x^{2} - 2) (x^{3} - 3 x)

5 x^{4} - 15 x^{2} + 6

解答ステップ

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

積の法則を適用:

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

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

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

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

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

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

簡素化

2 x (x^{3} - 3 x) + (3 x^{2} - 3) (x^{2} - 2) : 5 x^{4} - 15 x^{2} + 6

= 5 x^{4} - 15 x^{2} + 6