derivative (2x^2+5)(4x-1)

解

導関数

(2 x^{2} + 5) (4 x - 1)

24 x^{2} - 4 x + 20

解答ステップ

\frac{d}{d x} ((2 x^{2} + 5) (4 x - 1))

積の法則を適用:

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

f = 2 x^{2} + 5, g = 4 x - 1

= \frac{d}{d x} (2 x^{2} + 5) (4 x - 1) + \frac{d}{d x} (4 x - 1) (2 x^{2} + 5)

\frac{d}{d x} (2 x^{2} + 5) = 4 x

\frac{d}{d x} (4 x - 1) = 4

= 4 x (4 x - 1) + 4 (2 x^{2} + 5)

簡素化

4 x (4 x - 1) + 4 (2 x^{2} + 5) : 24 x^{2} - 4 x + 20

= 24 x^{2} - 4 x + 20