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

Why are the following not contradictory?

[tex]r=\sqrt{x^2+y^2}[/tex]

[tex]\frac{\partial r}{\partial x}=\frac{x}{\sqrt{x^2+y^2}}=\frac{x}{r}=cos{\theta}[/tex]

and

[tex] r=\frac{x}{cos{\theta}} [/tex]

[tex]\frac{\partial r}{\partial x}=\frac{1}{cos{\theta}}[/tex]

2. Relevant equations

3. The attempt at a solution

I understand that we got these results from differentiating two separate relations, but I don't see why they're different, and seemingly contradictory.

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# Homework Help: Polar Partials

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