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

解

導関数

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

24 x^{2} - 12 x + 12

解答ステップ

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

積の法則を適用:

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

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

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

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

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

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

簡素化

4 x (4 x - 3) + 4 (2 x^{2} + 3) : 24 x^{2} - 12 x + 12

= 24 x^{2} - 12 x + 12