`Ifu=sin^(- 1)(x/y)+tan^(- 1)(y/x),s h o w t h a tx(delu)/(delx)+y(delu)/(dely)=0`

If u=sin^(-1)((x+y)/(sqrtx+sqrty)) show that x(delu)/(delx)+y(delu)/(dely)=1/2 tan u.

If u = sin ^(-1) ((x ^(3) + y ^3)/(x-y)) show that x (del u)/(delx) + y (del u )/(del y) = 2 tan u.

If u =sqrt(x ^(4) +y ^(4)) show that x (delu)/(delx) + y ( del u)/(dely) =2u.

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

If u =tan^(-1)((x ^(4) +y ^(4))/(x ^(2)-y ^(2))) show that x (delu)/(delx) + y(del u)/(dely) = sin 2u.

Ifu = sin ^ (- 1) ((x) / (y)) + tan ^ (- 1) ((y) / (x)), showthat x (u) / (x) + y (u ) / (del y) = 0

If f(x,y) = 1/(sqrt(x^2+y^2)) then show that x(delf)/(delx)+y(delf)/(dely) = -f

If u= tan^-1((y^5)/(x^2)) , then find i. x((delu)/(delx)) + y((delu)/(dely)) ii. x^2((del^2u)/(delx^2))+2xy((del^2u)/(delxdely))+y^2((del^2u)/(dely^2))

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

If f = (x+y)/(sqrt(x-y)) then x (delf)/(delx) +y (delf)/(dely) is :