Question

which of the following expressions is the definition of the derivative of f(x)=ln(x) at the point (5,ln5)

Answer 1

The definition of the derivative is
$\frac{f(x + h) - f(x)}{h}$
as h goes to 0. So since the f is ln(x)

$\frac{ln(x+h)-ln(x)}{h}$

Since it is evaluated at 5 (the point 5, ln5), it is

$\frac{ln(5+h)-ln(5)}{h}$