" 11.Prove that "|[u,|,y],[u^(2),|^(2),y^(2)],[|+y,y+u,u+B]|=(beta-gamma)(gamma-u)(u-|)(u+beta+gamma)

If u=x/y^(2) - y/x^(2) , then

u=(x^(2)-y^(2))/(x^(2)+y^(2)) find d(u)/(dx)?

Let (x,y) = 2x y ^(2) + 3x ^(2) y calculate u _(x) (2,1) and u_(y) (1,-2).

Let alpha,beta,gamma are the real roots of the equation x^(3)+ax^(2)+bx+c=0(a,b,c in R and a!=0) If the system of equations (inu,v,andw) given by alpha u+beta v+gamma w=0 beta u+gamma v+alpha w=0gamma u+alpha v+beta w=0 has non-trivial solutions then the value of a^(2)/b is

Show that |[yz-x^2, zx-y^2, xy-y^2] , [zx-y^2, xy-z^2, yz-x^2] , [xy-z^2, yz-x^2, zx-y^2]|= |[r^2, u^2, u^2] , [u^2, r^2, u^2] , [u^2, u^2, r^2]| where r^2 = x^2+y^2+z^2 and u^2= xy+yz+zx

If u(x,y) =e^(x^(2) + y^(2)) , then (del u)/(del x) is equal to

If U(x,y,z) =(x^(2) + y^(2))/(xy) + 3z^(2)y , find (del U)/(dx) + (del U)/(dy) + (del U)/(dz)