## Seemingly Simple Derivative (as a limit) Problem

I'm having trouble showing the following:

lim [f(ax)-f(bx)]/x = f'(0)(a-b)
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) = (a-b)f(x).

Any ideas?

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 Recognitions: Gold Member Homework Help Science Advisor 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.
 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)...

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## Seemingly Simple Derivative (as a limit) Problem

Think chain rule..

 Recognitions: Gold Member Homework Help Science Advisor A further hint: Let g(x)=ax. Then, g(0)=0