I have a transformation $(x'_1,x'_2)=(f(x_1,x_2), g(x_1,x_2))$ and I wish to find $\partial x'_1\over \partial x'_2$ how might I evaluate this?
If it is difficult to find a general expression for this, what if we suppose $f,g$ are simply linear combinations of $x_1,x_2$ so something like $ax_1+bx_2$ where $a,b$ are constants?