Expressing A Quantity In Polar Coordinates?

[Xerxesshock2]

Homework Statement

Express the quantity ∂²/∂x²+∂²/∂y² in polar coordinates.

Homework Equations

x=ρcosφ
y=ρsinφ
ρ=sqrt(x²+y²)

The Attempt at a Solution

This is my first post, so I apologize for any weird looking equations, etc. I know that this is not a difficult problem, but I just cannot figure out exactly how to set it up. I don't know what function to differentiate for x and y... Any guidance would be appreciated. Thank you!

 

[jedishrfu]

Start by determining the first derivatives of x and y with respect to $\rho$ and $\phi$ and then repeat it for the second derivatives of x and y.

and please show your work. We can't help you without you showing your work.

Also try learning latex when entering your symbols for consistency with other posts here at PF.

We quote our expressions with double # front and back: #.#.\rho.#.# (remove the dots to see the rho as a greek letter)

Here's the PF reference:

https://www.physicsforums.com/threads/physics-forums-faq-and-howto.617567/#post-3977517

and here's a more extensive LaTex cheat sheet:

http://users.dickinson.edu/~richesod/latex/latexcheatsheet.pdf

 

[SteamKing]

Homework Statement

Express the quantity ∂²/∂x²+∂²/∂y² in polar coordinates.

Homework Equations

x=ρcosφ
y=ρsinφ
ρ=sqrt(x²+y²)

The Attempt at a Solution

This is my first post, so I apologize for any weird looking equations, etc. I know that this is not a difficult problem, but I just cannot figure out exactly how to set it up. I don't know what function to differentiate for x and y... Any guidance would be appreciated. Thank you!

∂²/∂x²+∂²/∂y² is not a quantity.

It is the Laplacian expressed in cartesian coordinates. (otherwise known as the ∇² operator)

http://hyperphysics.phy-astr.gsu.edu/hbase/lapl.html