derivative f(x)=(3x-10)(2x^2-x+1)

解

導関数

f (x) = (3 x - 10) (2 x^{2} - x + 1)

18 x^{2} - 46 x + 13

解答ステップ

\frac{d}{d x} ((3 x - 10) (2 x^{2} - x + 1))

積の法則を適用:

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

f = 3 x - 10, g = 2 x^{2} - x + 1

= \frac{d}{d x} (3 x - 10) (2 x^{2} - x + 1) + \frac{d}{d x} (2 x^{2} - x + 1) (3 x - 10)

\frac{d}{d x} (3 x - 10) = 3

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

= 3 (2 x^{2} - x + 1) + (4 x - 1) (3 x - 10)

簡素化

3 (2 x^{2} - x + 1) + (4 x - 1) (3 x - 10) : 18 x^{2} - 46 x + 13

= 18 x^{2} - 46 x + 13