Partial Derivative Matrix Proof

[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.

 

[statdad]

The notation stands for the determinant.

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

 

[losiu99]

As for the meaning: these are polar coordinates.

 

[critter]

Thanks!