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For which of the following does $\lim \limits_{h \to 0} \cfrac{f(x+h)-f(x)}{h}=e^x$?

$f(x)=\ln x$

$f(x)=\cfrac{1}{x+1} e^{x+1}$

$f(x)=e^x$

$f(x)=\cfrac{1}{e^x}$