finding transconductance for common source amplifier
for JFETs and long_channel MOSFETS, the Id = K/2 * (W/L) * Ve^2,
where Ve = Veffective = (Vgs - Vt)
Now you want the transconductance (or gm, which is a vacuum tube parameter that means conductivity_mutual or G_mutual)
Given gm is d_I_out / d_V_in, we simply take the derivative (use that calculus)
and we get
dId/dVe = K/2 * W/L * [ 2 * Ve^1]
or gm = dIdrain/dVgate =  K * W/L * Ve
where you can see a 10X higher Ve produces 10X the transconductance.