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

解

導関数

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

30 x^{2} - 50 x + 6

解答ステップ

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

積の法則を適用:

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

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

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

\frac{d}{d x} (5 x^{2} + 3) = 10 x

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

= 10 x (2 x - 5) + 2 (5 x^{2} + 3)

簡素化

10 x (2 x - 5) + 2 (5 x^{2} + 3) : 30 x^{2} - 50 x + 6

= 30 x^{2} - 50 x + 6