Rishita Asked a Question
May 12, 2020 5:00 pmpts 30 pts
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
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  • Ujjawal vishal thankyou
    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...j...
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  • Ujjawal vishal
    do you want proof of the theorem or just answer of that example...
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    Rishita
    i want proof ar basically want to understand theorem