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

$$T: x=u / v, y=v$$

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Missouri State University

University of Michigan - Ann Arbor

University of Nottingham

Idaho State University

All right, let's just find the Jacoby into the given transformation. So except you really wise v find Jacoby in. So, um, partial. With respect to X for you, it's one over v partial. Expect to the So from that this is equal to U times v to the negative one. So the derivatives directive, you'd be negative. You the to the negative to. And if we're gonna write negative exponents, I should just write everything they give exponents. So let's rewrite the first as such all right, and the impartial of wide stricter you zero partial y strategy is one else. We have to worry about that ugly part because then the determinant is the e to the negative one minus zero or just one over B. Check one thing that looks right. We should do that. Mistake. Yeah. So that's the determinant. One are That's true. But I want to be