?

AP® Calculus AB-BC

Free Version

Upgrade subject to access all content

Moderate

Evaluate Special Limit of Logarithmic Function

APCALC-W1V5EA

Let $f(x)=\lim \limits_{h \to 0} \frac{\ln (x+h)-\ln (x)}{h}$. What is $f'(a)$ for any fixed constant $a \gt 0$?

A

$\cfrac{1}{x}$

B

$e^a$

C

$e^x$

D

$\cfrac{1}{a}$