1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: Derivatives in polar coordinates

  1. Aug 21, 2010 #1
    I appologise in the lack of distinction between curly d's and infinitesimals! All derivatives are partial and anything outside of brackets is an infinitesimal.

    also, I sincerely apologise for any dodgy terminology, but I am for the most part self taught (regarding calculus) :/

    (also, 0 is my poor attempt to represent theta :P)

    1. The problem statement, all variables and given/known data

    More my obsessive compulsiveness when it's really something I'm just supposed to remember, but here goes...

    Express (dz/dx) in polar coordinates for some arbitrary z = z(r, 0)

    2. Relevant equations

    the answer given by my book (Steiner - The Chemistry Maths Book):

    (dz/dx) = (dz/dr)cos(0) - sin(theta)(1/r)(dz/d0)

    3. The attempt at a solution

    dz = (dz/dr)dr + (dz/d0)d0

    (dz/dx) = (dz/dr)(dr/dx) + (dz/d0)(d0/dx)

    essentially, my problem is in evaluating (dr/dx) and (d0/dx) (0 is theta)

    ATTEMPT AT EVALUATING (dr/dx)

    x = r cos(0) => r = x/cos(0)

    => (dr/dx) = 1/cos(0)

    which is... wrong :/. I've also tried so much more silly sh*t like implicit differentiation, and inverting dx/dr, always arriving at the same answer ):

    ATTEMPT AT EVAUATING (d0/dx)

    x = r cos(0) => 0 = arccos(x/r)

    and I have no idea how to start evaluating that...



    Any help anyone could give would be greatly appreciated! (:

    EDIT:

    I am an idiot... after 3 days of ploughing through with this and 10 minutes typing the problem to physicsforums, I just worked out that r can be represented in terms of x and y as sqrt(x^2 + y^2) and theta as arctan(y/x)... the rest writes itself lol :P

    I hate my life. :P
     
    Last edited: Aug 21, 2010
  2. jcsd
  3. Aug 21, 2010 #2

    lanedance

    User Avatar
    Homework Helper

    good that you've got it now, and sounds like a much easier method, but just to point out the reason this fell over, is becauser theta is a function of x & y also,
    so you must consider 0(x,y) when you take the derivative w.r.t. x
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook