implicit differentiation

[akoaysigod]

Compute dy/dt when y and z are determined as functions of t by the equations

y^5 + e^(yz) + zt^2 = 1
y^2 + z^4 = t^2

I have no idea how to go about doing this. I looked up some theorems but I didn't really understand them and they're not covered in this section of the book so I'm assuming they're not needed. I understand how this works for each equation individually, I think, but I don't really understand how this works with two equations like this. Anyway, I have a final on Friday and I'm pretty sure there will be something similar to this on it but I really have no idea, either way, it'd be good to know just in case.

Thanks

 

[wjm11]

There are 12 implicit differentiation problems of varying complexity completely worked out here:

http://www.math.ucdavis.edu/~kouba/...fsoldirectory/ImplicitDiffSol.html#SOLUTION 1

It should be helpful to study those.

 

[akoaysigod]

Thanks for the response but these all use the simple case of the implicit function theorem. Where dy/dx = - (dF/dx)/(dF/dy) which is pretty straight forward and I did a few problems like that already. I'm wondering how to apply this theorem to, or another method altogether, when there are multiple equations that need to be satisfied and more functions. I've had tremendous difficulties with this class and it's pretty much scared me away from analysis, and math in general.

Anyway, thanks for the reply.