The equations,
define x and y as functions of u and v. Find,
See figure attached for my attempt. It get's a little messy with the bottom determinant, so I'm not entirely convinced I've done this correctly.
Did I do anything wrong?
The equations,
define x and y as functions of u and v. Find,
See figure attached for my attempt. It get's a little messy with the bottom determinant, so I'm not entirely convinced I've done this correctly.
Did I do anything wrong?
Doing it by a slightly different method, I got almost the same answer. In fact, if you use implicit differentiation to differentiate each of the given equations partially with respect to v then you get
Write these equations as
Multiply the first equation by and the second by and subtract, to get
That is the same as your answer except that one of us has missed a minus sign somewhere, so that my denominator is the negative of yours.