1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Multivariable partial derivative

  1. Dec 7, 2015 #1
    1. The problem statement, all variables and given/known data
    From the transformation from polar to Cartesian coordinates, show that

    \begin{equation}
    \frac{\partial}{\partial x} = \cosφ \frac{\partial}{\partial r} - \frac{\sinφ}{r} \frac{\partial}{\partialφ}
    \end{equation}

    2. Relevant equations
    The transformation from polar to Cartesian coordinates is assumed to be x = r\cosφ

    3. The attempt at a solution
    To solve the problem i tried to use the multivariable chain rule. Resulting in the following equation:

    \begin{equation}
    \frac{\partial}{\partial x} =\frac{\partial r}{\partial x}\frac{\partial}{\partial r}+\frac{\partialφ}{\partial x}\frac{\partial}{\partial φ}
    \end{equation}

    Writing ##r = x/\cosφ## and ##\arccos(x/r) = φ## i tried to solve this problem. But this does not give the right answer.

    Am i using the right approach? I think it is necessary to use the multivariable chain rule in some form. But the partial derivative not acting on some other function seems a bit weird to me so i am not sure how to solve this problem.
     
    Last edited: Dec 7, 2015
  2. jcsd
  3. Dec 7, 2015 #2

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    In LaTeX, standard functions look a lot better if they are preceded by '\', so you get ##\sin \phi## instead of ##sin \phi##, etc.
     
  4. Dec 7, 2015 #3

    Samy_A

    User Avatar
    Science Advisor
    Homework Helper

    With that equation in mind:
    ##r=\sqrt{x²+y²}##
    ##φ=\arctan(\frac{y}{x})## (with some subtleties).
     
  5. Dec 8, 2015 #4
    Ahh, thanks a lot. That solved the problem.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted