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Multivariable Calculus

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Moderate

Evaluate Nonlinear 3D Jacobian

MVCALC-KXYZAJ

Evaluate the Jacobian $J(u,v,w)=\cfrac{\partial(x,y,z)}{\partial (u,v,w)}$ of the following transformation:

$$T: x=wv, y=wu, z=u^2+v^2$$

A

$2uvw+2wv^2$

B

$uvw+wv^2$

C

$uw+v^2$

D

$uvw$

E

$u^2v^2w^2$