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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)
    ∂z/∂x=2xyf(x^2-y^2)

    i was able to prove that
    x(∂z/∂y)+y(∂z/∂x)=xz/y

    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

    LCKurtz

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    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

    NascentOxygen

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