Anonymous posted an Question
May 12, 2020 • 22:30 pm 30 points
  • IIT JAM
  • Mathematics (MA)

Theorem : suppose that f(x,x,..x)is a rea-valued function such that f and all of its partial derivatives of order less than or equal to r are defined and contin

Theorem : Suppose that f(x,x,..X)is a rea-valued function such that f and all of its partial derivatives of order less than or equal to r are defined and continuOus on an open subset u of R". Then, at each point p in u, every partial derivative of order r is independent of the order in which the partial derivatives are calculated. Example. Suppose that T(X,y.2)= *y°2 + xe" + y' sin(3x - 52). Then, Theorem implies that 0f ôzÖYÔX čZÖXÖYÔX x ôy©z which are equal to every other 4th order partial derivative that's with respect to x twice, and y and Z once each. ntoot lle + W IColl Toll Eroo: 1800 1

1 Answer(s) Answer Now
  • 0 Likes
  • 2 Comments
  • 0 Shares
  • comment-profile-img>
    Ujjawal vishal best-answer

    order is not important in partial derivatives.. if you differentiate(partially) w.r.t x first and then it by y or you do it first w.r.t y and then by x you will get same result...just solve some examples

  • comment-profile-img>
    Ujjawal vishal

    do you want proof of the theorem or just answer of that example...

    eduncle-logo-app

    i want proof ar basically want to understand theorem

whatsapp-btn

Do You Want Better RANK in Your Exam?

Start Your Preparations with Eduncle’s FREE Study Material

  • Updated Syllabus, Paper Pattern & Full Exam Details
  • Sample Theory of Most Important Topic
  • Model Test Paper with Detailed Solutions
  • Last 5 Years Question Papers & Answers