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Diffrentiability of function with two variable

  1. Feb 3, 2013 #1
    Hii plz help me to Solve problems diffrentiability of function with two variable with one method.
     
  2. jcsd
  3. Feb 3, 2013 #2

    tiny-tim

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    Welcome to PF!

    Hi The Rahul! Welcome to PF! :smile:

    Show us one or two examples that you've had difficulty with, together with your attempts to solve them. :wink:
     
  4. Feb 3, 2013 #3

    Evo

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    Staff: Mentor

    The Rahul, you just sent your reply to the mentor's forum. I'm reposting it here for you. To reply, please use either the "quote" button on the bottom right, or "New Reply", not "report".

     
  5. Feb 3, 2013 #4
    Re: Welcome to PF!

    Hii Tiny tim,thnx for ur warm welcome,
    Now I continue my problem=
    In this Ques.—f(x,y)={|xy|}1/2 Not differentiable at (0,0)
    I find out Both Partial derivative fx and fy and solve the ques.
    But in that ques.== f(x,y)= xy /√(x2+y2)
    in my book method is diffrent.
    in that ques method is to find according to y=mx and x=y3.
    so Plz help me....:-D
     
  6. Feb 3, 2013 #5

    tiny-tim

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    Hi The Rahul! :smile:

    To prove that a function f(x,y) is not differentiable at (0,0),

    we only need to find one curve along which it is not differentiable (and then we can stop).

    If f(x,y) = xy /√(x2+y2) = xy/r,

    then the derivative along any straight line does exist at (0,0), so we can't stop there, we need to check other ways of approaching the origin …

    in this case, the easiest curve to check is x=y3 (or y=x3) :wink:

    (x=y2 is awkward, because it gives you awkward square-roots

    btw, since you've woken the mentors :wink:, please note that txt-english (eg "plz", "ur") is against the forum rules! :bugeye:
     
  7. Feb 4, 2013 #6

    Thank you for your precious reply.It works.:smile:
     
  8. Feb 4, 2013 #7

    HallsofIvy

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    Ah, yes! Let sleeping mentors lie! We are very grouchy until we have had our coffee. (Except for evo, of course.)
     
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