# A proof involving Jacobians

1. Sep 14, 2009

### primrosewater

1. The problem statement, all variables and given/known data

Prove that J(s,t/x,y)*J(x,y/s,t)=1 (Hint: Multiply the determinants).

2. Relevant equations

Definition of a Jacobian.

3. The attempt at a solution

I found the determinants and multiplied them. Now I have a FOILed equation of partial derivatives and no idea where to go from there. If I'm missing some underlying mathematical fact involving partials or Jacobians that everyone "knows," I'd appreciate it if someone would tell me anything at all. I don't know where to go beyond the hint at all.

2. Sep 15, 2009

### gabbagabbahey

$$\frac{\partial a}{\partial b}\frac{\partial b}{\partial a}=1$$

Does that help?