" If "u(x+y)=(x^(2)+y^(2))," prove that "((del u)/(del x)-(del u)/(del y))^(2)=4(1-(del u)/(del x)-(del u)/(del y))

If u (x,y) =x ^(2) + 2xy-y ^(2) then (del u)/(del x) + (delu)/(del y) is:

If u=(x^(2)+y^(2)+z^(2))^(-1/2) show that x(del u)/(del x)+y(del u)/(del y)+z(del u)/(del z)=-u

If u=(x^(2)+y^(2)+z^(2))^(-1/2) show that x(del u)/(del x)+y(del u)/(del y)+z(del u)/(del z)=-u

If u(x,y) = (x^(2) + y^(2))/sqrt(x+y) , prove that x(del u)/(del x) + y(del u)/(del y) = 3/2 u .

If v(x,y) = log((x^(2) +y^(2))/(x+y)) , prove that x(del v)/(del x) + y(del v)/(del y)=1 .

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

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

If z (x + y) = x ^ (2) + y ^ (2) show that [(del z) / (del x) - (del z) / (del y)] ^ (2) = 4 [1 - (del z) / (del x) - (del z) / (del y)]

If u = cos ^(-1) ((x)/(y)) prove that x (del u)/(delx) + y (del u)/(dely)=0.