Seemingly Simple Derivative (as a limit) Problemby luke8ball Tags: derivative, limit, seemingly, simple 

#1
Nov2012, 02:01 PM

P: 22

I'm having trouble showing the following:
lim [f(ax)f(bx)]/x = f'(0)(ab) x→0 I feel like this should be really easy, but am I missing something? I tried to use the definition of the derivative, but I know I can't just say f(ax)f(bx) = (ab)f(x). Any ideas? 



#2
Nov2012, 02:04 PM

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Try to add zero in your numerator in the shape f(0)f(0), and see if you can rearrange it in a clever manner.




#3
Nov2012, 02:11 PM

P: 22

You mean so that I get:
[lim f(ax)  f(0)]/x  [lim f(bx)  f(0)]/x x→0 x→0 I had thought about that, but I still don't see how that gives me af'(0)  bf'(0)... 



#4
Nov2012, 02:20 PM

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Seemingly Simple Derivative (as a limit) Problem
Think chain rule..




#5
Nov2012, 03:05 PM

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A further hint:
Let g(x)=ax. Then, g(0)=0 


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