JFET Vgs Calculation Equation
Following up on Andy's link, we differentiate the equation # 6.39,
with respect to \$V_{DS}\$.

We want the resistance. That requires incremental \$V_\mathrm{Drain}/I_\mathrm{Drain}\$.

We end up with a constant portion: 
$$
\frac{\mathrm{d}I_D}{\mathrm{d} V_{DS}} = 2 K (V_{GS} - V_P)
$$
and a variable portion: 
$$
\begin{split}
\frac{\mathrm{d}I_D}{\mathrm{d} V_{DS}} &amp;= K 2 (2 V_{DS}) \\
&amp;= 4 K V_{DS}
\end{split}
$$
The constant portion is the transconductance, or the inverse of channel resistance.

The variable portion is the DISTORTION.