Is the following statement true or false? If true, please provide a proof. if false, please provide a counter example.

If f is differentiable on $$ and

$[\backslash$lim$\_\{$x$\backslash$rightarrow $5\}\backslash$frac$\{2$x$\}\{$f$\text{'}($x$)\}=1,]$

then

$[\backslash$lim$\_\{$x$\backslash$rightarrow $5\}\backslash$frac$\{$x$^2\}\{$f$($x$)\}=1.]$