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

2. Relevant equations

This should be easy, I don't know what I've done wrong...

polar coordinates

[tex]x=r cos(\theta)[/tex]

[tex]y=r sin(\theta)[/tex]

[tex]r^2=x^2+y^2[/tex]

3. The attempt at a solution

so with [tex]x=r cos(\theta)[/tex]

[tex] \partial{x}/\partial{r}=cos(\theta) [/tex]

[tex] \partial{x}/\partial{r}=x/r [/tex]

thus the inverse

[tex] \partial{r}/\partial{x}=r/x [/tex]

similarly with [tex]r=x/cos(\theta)[/tex]

partial of r wrt x

I get

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

[tex]

\partial{r}/\partial{x} = r/x

[/tex]

now doing same thing on the r^2 equation

partial of r wrt x

[tex]

2r\partial{r}/\partial{x}=2x

[/tex]

[tex]

\partial{r}/\partial{x}=x/r

[/tex]

what the heck? why am I getting two different (and inverse) answers from these two related equations?

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# This should be an easy partial derivative

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