derivative (x^2-18)(2x+3)

解

導関数

(x^{2} - 18) (2 x + 3)

6 x^{2} + 6 x - 36

解答ステップ

\frac{d}{d x} ((x^{2} - 18) (2 x + 3))

積の法則を適用:

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

f = x^{2} - 18, g = 2 x + 3

= \frac{d}{d x} (x^{2} - 18) (2 x + 3) + \frac{d}{d x} (2 x + 3) (x^{2} - 18)

\frac{d}{d x} (x^{2} - 18) = 2 x

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

= 2 x (2 x + 3) + 2 (x^{2} - 18)

簡素化

2 x (2 x + 3) + 2 (x^{2} - 18) : 6 x^{2} + 6 x - 36

= 6 x^{2} + 6 x - 36