derivative (6x+5)(x^2-3x)

解

導関数

(6 x + 5) (x^{2} - 3 x)

18 x^{2} - 26 x - 15

解答ステップ

\frac{d}{d x} ((6 x + 5) (x^{2} - 3 x))

積の法則を適用:

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

f = 6 x + 5, g = x^{2} - 3 x

= \frac{d}{d x} (6 x + 5) (x^{2} - 3 x) + \frac{d}{d x} (x^{2} - 3 x) (6 x + 5)

\frac{d}{d x} (6 x + 5) = 6

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

= 6 (x^{2} - 3 x) + (2 x - 3) (6 x + 5)

簡素化

6 (x^{2} - 3 x) + (2 x - 3) (6 x + 5) : 18 x^{2} - 26 x - 15

= 18 x^{2} - 26 x - 15