[微積] f(x+y) = f(x)f(y) implies f(x) = a^x
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)
但是還是看不出來 ----- 是constant
f(x)
請問這題要怎麼做呢?
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