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!

Unusual partial differentiation equation

  1. Oct 22, 2012 #1
    1. The problem statement, all variables and given/known data

    Calculate ∂f/∂x and ∂f/∂y for the following function:

    [itex]yf^2 + sin(xy) = f [/itex]

    3. The attempt at a solution

    I understand basic partial differentiation, but I have no idea how to approach the f incorporation on both sides of the equation nor what you would explicitly call this kind of mathematical technique. Anyone who can point me in the right direction?
     
  2. jcsd
  3. Oct 22, 2012 #2

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    welcome to pf!

    hi rachibabes! welcome to pf! :smile:
    just do ∂/∂x to the equation in the usual way (using the product rule for the yf2) …

    what do you get? :smile:
     
  4. Oct 23, 2012 #3
    [itex]yf^2 + sin(xy) = f [/itex]

    I get:

    [itex]y2f∂f/∂x +f^2∂y/∂x + cos(xy)*(x∂y/∂x+y) = ∂f/∂x [/itex]

    [itex]y2f∂f/∂x +f^2∂y/∂x + x∂y/∂xcos(xy) + ycos(xy) = ∂f/∂x[/itex]

    [itex]∂y/∂x[f^2 + cos(xy)] + ycos(xy) + y2f∂f/∂x = ∂f/∂x[/itex]

    I have no idea how to remove the ∂f/∂x on the left hand side :/
     
  5. Oct 23, 2012 #4

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    hey there, rachibabes! :smile:

    (just got up :zzz:)

    f(x,y) is a function of the variables x and y

    ∂/∂x means differentiating wrt x keeping y fixed

    so ∂y/∂x = … ? :smile:
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Unusual partial differentiation equation
Loading...