Re: Maths ! help !

Posted by Granpa Simpson on Apr 19, 2014; 8:54am
URL: http://discussion-forum.276.s1.nabble.com/Maths-help-tp7587407p7587431.html

By using Euler’s Theorem, n*f(x,y)=x*fx+y*fy
Again differentiating partially wrt x and y respectively we get,
Or, n*fx = fx + x*fxx +  y*fyx...................(1)
Or, n*fy = fy + y*fyy +  x*fxy………………...(2)
By using Young’s Theorem fxy = fyx.
Multiplying (1) by x, (2) by y and adding and rearranging we get.
n*(x*fx + y*fy)= (x^2)*fxx+ (y)^2*fyy+ 2*x*y*fxy + (x*fx+y*fy)
Substituting x*fx+y*fy = nf we get,
n*n*f - n*f = (x^2)*fxx+ (y)^2*fyy+ 2*x*y*fxy .
or, (x^2)*fxx+ (y)^2*fyy+ 2*x*y*fxy = n*f*(n-1)