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

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 f=x/(x^(2) + y^(2)) , then show that x (del f)/(del x) + y(del f)/(del y) =-f .

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

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

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

If u= x^3-3xy^2 , show that (del^2u)/(delx^2)+(del^2u)/(dely^2) =0

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- y/x^2 , show that (del^2u)/(delxdely)=(del^2u)/(delydelx) .