Ok, so not really partials, I know how to do those. But now in my math physics class we were introduced to a new notation where it's the partial with respect to a variable, with another variable held constant. This is the problem I am trying to do in the book:(adsbygoogle = window.adsbygoogle || []).push({});

[tex](\frac{\partial z}{\partial \theta})_x[/tex]

Where [tex]z = x^2 + 2y^2 , x = r cos(\theta) , y = r sin(\theta)[/tex]

The answer in the book gives me [tex]4 r^2 tan(\theta)[/tex]

Now, am I missing something here? All the examples in the book (a whole quarter of a page... it's a crappy book...) specifically set up the equation to be in terms of the two variables (denominator and subscript) before taking the partial derivative. But this answer gives me an r? And a TANGENT!? I can't conceive of how to do this. I've been at it for a few hours.

I've tried things like transforming everything into polar first. Or only the x's. Or only the y's. Or going [tex] 2x^2 + 2y^2 - x^2[/tex] and then transforming it all. Nothing. I can't get close to a tangent.

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# Partial Derivatives

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