1. ## Cylindrical Coordinates

$f(x,y)=\frac{x^2+y^2}{e^{x^2+y^2}}$

I need to write an equation for this in cylindrical coordinates.

I know that $r^2=x^2+y^2$ and $x=rcos\theta$
$y=rsin\theta$

if I directly substituted I would end up with,

$\frac{r^2}{e^{r^2}}$

Am I even close?

2. Hello, Jesse!

I'll modify your work slightly . . .

$f(x,y)\:=\:\frac{x^2+y^2}{e^{x^2+y^2}}$
Write in cylindrical coordinates.
We have: . ${\color{blue}z \;=\;\frac{x^2+y^2}{e^{x^2+y^2}}}$

I know that: . $\begin{array}{ccc}r^2 &=&x^2+y^2 \\ x & = &r\cos\theta \\ y &=&r\sin\theta \\
{\color{blue}z} &{\color{blue}=}& {\color{blue}z} \end{array}$

Substituting, I end up with: . ${\color{blue}z} \;=\;\frac{r^2}{e^{r^2}}\qquad{\color{red}\hdots\; \;Right!}$