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

解

導関数

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

30 x^{2} + 50 x + 2

解答ステップ

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

積の法則を適用:

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

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

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

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

\frac{d}{d x} (5 x^{2} + 1) = 10 x

= 2 (5 x^{2} + 1) + 10 x (2 x + 5)

簡素化

2 (5 x^{2} + 1) + 10 x (2 x + 5) : 30 x^{2} + 50 x + 2

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