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

解

導関数

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

24 x^{2} - 24 x + 6

解答ステップ

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

積の法則を適用:

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

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

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

\frac{d}{d x} (4 x^{2} + 3) = 8 x

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

= 8 x (2 x - 3) + 2 (4 x^{2} + 3)

簡素化

8 x (2 x - 3) + 2 (4 x^{2} + 3) : 24 x^{2} - 24 x + 6

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