Proof involving limit of derivative

1. The problem statement, all variables and given/known data

give an example of a function f for which lim f(x) as x[tex]\rightarrow[/tex][tex]\infty[/tex] exists, but lim f'(x) as x[tex]\rightarrow[/tex][tex]\infty[/tex] does not exist.

2. Relevant equations

f'(x) = lim [f(x+h)-f(x)]/h as h[tex]\rightarrow[/tex]0

3. The attempt at a solution

for some reason, i can only seem to find equations where lim f(x) as x[tex]\rightarrow[/tex][tex]\infty[/tex] does not exist, but lim f'(x) as x[tex]\rightarrow[/tex][tex]\infty[/tex] does exist. ex.f(x)=x and f'(x)=1
Try thinking of functions that require the chain rule to find the derivative.
i.e. Let [itex]f(x) = g(h(x))[/itex]. Then [itex]f'(x) = g'(h(x)) \cdot h'(x)[/itex].

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