Anyone have time to check my Jacobian for this transformation?

[Theelectricchild]

Anyone have time to check my Jacobian for this transformation!?

$$x = e^{u-v}$$ $$y = e^{u+v}$$ $$z = e^{u+v+w}$$

I ended up getting the Jacobian as ZERO.

This is why I am doubting myself--- it seems wrong! What do you guys get?

Thanks for you help.

 

[ReyChiquito]

the jacobian isn't zero, check your calculations, you might have a bad sign...

 

[Theelectricchild]

Yeah i screwed up --- i got something like 2^(u-v) * (e^2u+2v+w)

does that look oK?

 

[Theelectricchild]

whoops i mean [2*e^(u-v)] * [(e^2u+2v+w)]

 

[HallsofIvy]

You still may be off: I get 2e^u+v+we^2u= 2e^3u+v+w.

(Edited after jdavel pointed out an error.)

 

[jdavel]

Halls of Ivy,

You have a typo in your final answer. That should be 3u, not 2u.

Theelectricchild, to keep from confusing the signs, it helps (at least in this case, since exp(x) is its own derivative) to find all nine derivates and then write the determinant in terms of x, y and z. Then, with those two beautiful zeros, the Jacobian = 2xyz is almost staring you in the face.

 

[Theelectricchild]

Thx for your help guys--- I find this class a big leap in difficulty from where we left off in our calculus III course which was on tangent planes--- I am glad I am getting help. Ugh now to get ready for Friday's midterm.