derivative (x^2-12)(2x-9)

解

導関数

(x^{2} - 12) (2 x - 9)

6 x^{2} - 18 x - 24

解答ステップ

\frac{d}{d x} ((x^{2} - 12) (2 x - 9))

積の法則を適用:

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

f = x^{2} - 12, g = 2 x - 9

= \frac{d}{d x} (x^{2} - 12) (2 x - 9) + \frac{d}{d x} (2 x - 9) (x^{2} - 12)

\frac{d}{d x} (x^{2} - 12) = 2 x

\frac{d}{d x} (2 x - 9) = 2

= 2 x (2 x - 9) + 2 (x^{2} - 12)

簡素化

2 x (2 x - 9) + 2 (x^{2} - 12) : 6 x^{2} - 18 x - 24

= 6 x^{2} - 18 x - 24