Thanks very much for the reply; with that info:
\frac{di_1}{dq_1} = 2q_1+1
\frac{dv_1}{dq_1} = U_T(\frac{2q_1+1}{q_1})
And from this I get
\frac{di}{dv}=\frac{ \frac{di_1}{dq_1} }{ \frac{dv_1}{dq_1} }= \frac{q_1}{U_T}
I'm not sure if this is correct. For one thing, I'm not sure how I could...
This isn't a homework problem exactly but my attempt to derive a result given in a textbook for myself. Below is my attempt at a solution, typed up elsewhere with nice formatting so didn't want to redo it all. Direct image link here. Would greatly appreciate if anyone has any pointers.