展開する ln(ax+b)2x(ax+b)

解

展開する

ln (a x + b) \cdot 2 x \cdot (a x + b)

2 a x^{2} ln (a x + b) + 2 b x ln (a x + b)

解答ステップ

ln (a x + b) \cdot 2 x (a x + b)

= 2 x ln (a x + b) (a x + b)

分配法則を適用する:

a (b + c) = ab + a c

a = ln (a x + b) \cdot 2 x, b = a x, c = b

= ln (a x + b) \cdot 2 x a x + ln (a x + b) \cdot 2 x b

= 2 a xx ln (a x + b) + 2 b x ln (a x + b)

2 a xx ln (a x + b) = 2 a x^{2} ln (a x + b)

= 2 a x^{2} ln (a x + b) + 2 b x ln (a x + b)