derivative y=(3x^2+2)(2x-5)

解

導関数

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

18 x^{2} - 30 x + 4

解答ステップ

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

積の法則を適用:

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

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

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

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

\frac{d}{d x} (2 x - 5) = 2

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

簡素化

6 x (2 x - 5) + 2 (3 x^{2} + 2) : 18 x^{2} - 30 x + 4

= 18 x^{2} - 30 x + 4