This page

Rpi - Input resistance of a transistor

Simple amplifier circuit

Equivalent scematics:

So how can a diode have resistance?

Shockley equation:

Shockley equation is diode current as a function of diode voltage.

Id - diode current
Vd - diode voltage
Is - reverse bias saturation current
Vt - termal voltage
n - ideality factor

Diode allmoast constant current changes just a little bit under the influence of input signal.
Because this change is small, it can be approximated with a line.
Slope of this line is input resistance Rpi.
Slope of a tangent line is first derivative.

Rpi is resistance that input signal sees when it is connected to amplifier input.
We model base-emmiter junction of a transistor with a diode.
This diode inside amplifier circuit is allways biased and has current Id trough it.
Input signal will change this current just a little bit, so we can approximate
diode function with tangent line, and because amplifier has input capacitor
we are only interested in the slope of that line.
Slope of a tangent line to function at certain point, is first derivative at that point.
And this is Rpi.

By the way formula for Vt is:

k - Boltzmann constant
T - temperature of diode in Kelvins
q - elementary charge