作者GSXSP (Gloria)
看板Math
标题[微积] f(x+y) = f(x)f(y) implies f(x) = a^x
时间Sat Feb 12 10:37:19 2011
f(x) differentiable on (-∞,∞)
with f(x+y) = f(x)f(y)
prove that f(x) = a^x for some a
(Hint: ln f(x) must have constant derivitive)
我做 f'(x) f'(y)
grad ln f(x+y) = (------ , ------ )
f(x) f(y)
f'(x)
但是还是看不出来 ----- 是constant
f(x)
请问这题要怎麽做呢?
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◆ From: 218.168.28.40
1F：→ yhliu :(d/dx)ln(f(x+a)) = (d/dx)ln(f(x)) for any a in R. 02/12 10:57
2F：推 wayne2011 :Use differential definition to solve it. 02/12 10:58
3F：→ GSXSP :Oh! 原来这样看 谢谢 02/12 11:26