Solving for Partials: ∂u/∂x Explained

[Zeth]

"Solving for Partials"

This is for my revision and I have the answer sheet:

I'm meant to find ∂u/∂x for x = u + v + w, y = u^2 + v^2 + w^2, z = u^3 + v^3 + w^3

That as far as I can tell, by a miracle, is meant to equal:

∂u/∂x=(vw)/((v − u)(w − u))

All the question says apart from find this is "Solving for Partials".

I can't find anything that looks like this in my notes and google comes up empty. What's going on here?

 

[Hurkyl]

Well, if you want to solve for the partial derivative of u with respect to x, it seems that you ought to partially differentiate each equation with respect to x. What kind of equations do you get when you do that?

 

[ice109]

key word : implicit differentiation