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

Given Cartesian coordinates x, y, and polar coordinates r, phi, such that

[tex]r=\sqrt{x^2+y^2}, \phi = atan(x/y)[/tex] or

[tex]x=r sin(\phi), y=r cos(\phi)[/tex]

(yes, phi is defined differently then you're used to)

I need to find [tex]\frac{d\phi}{dr}[/tex] in terms of [tex]\frac{dy}{dx}[/tex]

2. Relevant equations

All given in part 1

3. The attempt at a solution

I tried to compute [tex]\frac{d \phi}{d r}[/tex] directly and ended up with this:

[tex]\frac{d \phi}{d r} = \frac{d \phi}{d x} \frac{d x}{d r} + \frac{d \phi}{d y} \frac{d y}{d r}

= \frac{y}{x^2+y^2} sin{\phi} - \frac{x}{x^2+y^2} cos{\phi}\\

= \frac{y}{x^2+y^2} \frac{x}{\sqrt{x^2+y^2}} - \frac{x}{x^2+y^2} \frac{y}{\sqrt{x^2+y^2}}\\

= 0[/tex]

Obviously this isn't correct, so I must be going about this the wrong way.

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# Homework Help: Converting partial derivatives between coordinate frames

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