(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find

[tex] \frac{\partial z}{\partial y} [/itex]

where z=F(u,v,y), u=f(v,x), v=g(x,y).

3. The attempt at a solution

If I remember multivariate calculus at all, this should be (please forgive the abuse of notation)

[tex] \frac{\partial z}{\partial y} = \frac{\partial z}{\partial u}\frac{\partial u}{\partial v}\frac{\partial v}{\partial y} + \frac{\partial z}{\partial v}\frac{\partial v}{\partial y} + \frac{\partial z}{\partial y} [/tex]

However, I have a book in front of me that says it should be

[tex] \frac{\partial z}{\partial y} = \frac{\partial z}{\partial v}\frac{\partial v}{\partial u}\frac{\partial u}{\partial y} + \frac{\partial z}{\partial u}\frac{\partial u}{\partial y} + \frac{\partial z}{\partial y} [/tex]

I think I'm correct and that they must have confused u and v. If someone could verify this for me it would be much appreciated.

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# Homework Help: Multivariate Chain Rule

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