derivative (3x^2-1)(2x+3)

解

導関数

(3 x^{2} - 1) (2 x + 3)

18 x^{2} + 18 x - 2

解答ステップ

\frac{d}{d x} ((3 x^{2} - 1) (2 x + 3))

積の法則を適用:

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

f = 3 x^{2} - 1, g = 2 x + 3

= \frac{d}{d x} (3 x^{2} - 1) (2 x + 3) + \frac{d}{d x} (2 x + 3) (3 x^{2} - 1)

\frac{d}{d x} (3 x^{2} - 1) = 6 x

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

= 6 x (2 x + 3) + 2 (3 x^{2} - 1)

簡素化

6 x (2 x + 3) + 2 (3 x^{2} - 1) : 18 x^{2} + 18 x - 2

= 18 x^{2} + 18 x - 2