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Compute the Jacobian $J(u, v)$ for the following transformations.

$$T: x=2 u v, y=u^{2}-v^{2}$$

$-4\left(u^{2} + v^{2}\right)$

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Oregon State University

Harvey Mudd College

University of Michigan - Ann Arbor

University of Nottingham

All right. So we're supposed to calculate the Jacoby in for the given transformation. So let's go through. Conquer the partial derivatives. A partial X district to you is to be partial X prospective e is to you partial. Why respect to you is to you partial vice for TV is negative. Two V botched the negative there. So the determinant that is negative for the squared minus for you squared and we're done.