Equivalent Small-Signal Resistance of a MOSFET Circuit

[NHLspl09]

Homework Statement

Derive an expression for the equivalent small-signal conductance G_eq (or resistance R_eq).

Homework Equations

G_eq = $\frac{i_t}{v_t}$

v_t = v_g

v_s = 0

v_d = -v_t

The Attempt at a Solution

Attachment - EE HW 2

I drew the small-signal circuit, from what I gather it seems to be correct although I am a bit rusty on that. I began by using KCL at node v_g and solving for G_eq but I'm really unsure as to whether I've started this right. Looking at my work so far, to me, it seems to be on track for solving for G_eq. If someone could just simply check my work/small-signal model over from what I have so far it would be greatly appreciated to earn some confidence on continuing my work! Thank you.

 

[NHLspl09]

Anyone have any insight on finding this equivalent resistance? I've been trying to use KCL but my answer continues to look even worse. Any help or insight would be greatly appreciated!