# Given the Function: f:RR^2 to RR^2 , r in RR. f(x,y)={x=r cos(theta)y=r sin(theta)Calculate this Partial Derivative: (del(x,y))/(del(r,theta))

Given the Function:
$f:{\mathbb{R}}^{2}\to {\mathbb{R}}^{2}$ , $r\in \mathbb{R}.$
$f\left(x,y\right)=\left\{\begin{array}{l}x=r\mathrm{cos}\left(\theta \right)\\ y=r\mathrm{sin}\left(\theta \right)\end{array}$
Calculate this Partial Derivative:
$\frac{\mathrm{\partial }\left(x,y\right)}{\mathrm{\partial }\left(r,\theta \right)}$
I do really need some help on this lads, any help would be really appreciated.
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kregde84
This symbol is shorthand for the Jacobian matrix
$\left[\begin{array}{cc}\frac{\mathrm{\partial }x}{\mathrm{\partial }r}& \frac{\mathrm{\partial }x}{\mathrm{\partial }\theta }\\ \frac{\mathrm{\partial }y}{\mathrm{\partial }r}& \frac{\mathrm{\partial }y}{\mathrm{\partial }\theta }\end{array}\right]$