# Partial Derivative Matrix Proof

1. Sep 24, 2010

### critter

x=rcos(θ), y=rsin(θ) Do these formulas look familiar? They give the relationship between two coordinate systems in the plane. Evaluate:
|x'r x'θ|

|y'r y'θ|

I know that the x primes are cos(θ) and -rsin(θ), and the y primes are sin(θ) and rcos(θ), respectively. I am not sure what to do with the matrix. The original functions do look familiar, but I do not remember what they mean.

2. Sep 24, 2010

The notation stands for the determinant.

[tex]
\left|\begin{matrix} a& b \\ c & d \end{matrix} \right|= ad - bc
[/itex]

3. Sep 25, 2010

### losiu99

As for the meaning: these are polar coordinates.

4. Sep 25, 2010

Thanks!