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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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##### Heather Z.

Oregon State University

##### Kristen K.

University of Michigan - Ann Arbor

##### Samuel H.

University of Nottingham

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### Video Transcript

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.

##### Heather Z.

Oregon State University

##### Kristen K.

University of Michigan - Ann Arbor

##### Samuel H.

University of Nottingham

Lectures

Join Bootcamp