If `u=(x^2+y^2)/(x+y)`, prove that `((delu)/(delx)-(delu)/(dely))^2=4(1-(delu)/(delx)-(delu)/(dely))`

If u = (x^2+y^2+z^2)^(-1/2) then prove that (del^2u)/(delx^2)+(del^2u)/(dely^2)+(del^2u)/(delz^2) =0

If u=log(x^(2)+y^(2)+z^(2)) prove that (del^(2)u)/(del x^(2))+(del^(2)u)/(del y^(2))+(del^(2)u)/(del z^(2) = 2/(x^(2)+y^(2)+z^(2)

If u = log ((x ^ (2) + y ^ (2)) / (x + y)), prove that x (u) / (x) + y (u) / (y) = 1

If y=x+(1)/(x+(1)/(x+(1)/(x+1))), prove that (dy)/(dx)=(y)/(2y-x)

if sin^(-1)((x^(2)-y^(2))/(x^(2)+y^(2)))=c prove that (dy)/(dx)=(y)/(x)

Select the correct statements for ideal gases: 1. ((delH)/(delT))_(P)-((delU)/(delT))_(V)=R 2. ((delH)/(delT))_(P)-((delU)/(delT))_(P)-((delU)/(delT))_(V) =work done 3. ((delU)/(delV))_(T)=+ve 4. ((delT)/(delP))_(H)=+ve

If sqrt(1-x^(2))+sqrt(1-y^(2))=a(x-y), prove that (dy)/(dx)=sqrt((1-y^(2))/(1-x^(2)))

If sqrt(1-x^(2))+sqrt(1-y^(2))=a(x-y), prove that (dy)/(dx)=sqrt((1-y^(2))/(1-x^(2)))

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

If tan ^(-1)((x^(2)-y^(2))/(x^(2)+y^(2)))=a, prove that (dy)/(dx)=(x)/(y)((1-tan a))/((1+tan a))