if $f’(x)/g’(x) = f(x)/g(x)$, what can we say about the relationship? Suppose for all $x$,
$$f’(x)/g’(x) = f(x)/g(x),$$
Then what can we say about the relationship between $f(x)$ and $g(x)$?
I think the only solution is $f(x) = cg(x)$ for some non-zero constant $c$. Is there any other possible relationship?

Then the numerator of quotient rule for derivative of $f/g$ vanishes and so $f/g$ constant. Need to do more work on it for  proof...
