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: Basic partial differentiation help (needs checking)

  1. Mar 26, 2012 #1
    1. The problem statement, all variables and given/known data
    given z=yf(x^2-y^2)
    show that the x(∂z/∂y)+y(∂z/∂x)=xz/y

    3. The attempt at a solution

    cut it short, my
    ∂z/∂y= f(x^2-y^2)-2(y^2)f(x^2-y^2)

    i was able to prove that

    But i need help with partial differentiations when they give an equation like z=f(x^2-y^2)
    I've read about partially differentiating such equations somewhere before. Can someone please check if i am doing it right? Also, what is this kind of partial differentiation called? (such as partially differentiating z=f(x^2-y^2)
    I would really appreciate if someone could tell me what is it called so i could read up more about it and do more examples of this kind.
  2. jcsd
  3. Mar 26, 2012 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    When you have something like ##z=f(x^2-y^2)## you need to use the chain rule. The easiest way to see this is to look at as ##z = f(u),\ u=x^2-y^2## Now if you want to calculate ##z_x## you use$$
    z_x = f'(u)u_x = f'(x^2-y^2)(-2x)$$You are missing the primes in your argument.
  4. Mar 26, 2012 #3


    User Avatar

    Staff: Mentor

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook