If `x=rcosthetaandy=rsintheta` , prove that `(del^2r)/(delx^2)+(del^2r)/(dely^2)=1/r[((delr)/(delx))^2+((delr)/(dely))^2]`

If x = r cos theta and y = r sin theta, prove that (del ^ (2) r) / (del x ^ (2)) + (del ^ (2) r) / (del y ^ (2)) = (1) / (r) [((del r) / (del x)) ^ (2) + ((del r) / (del y)) ^ (2)]

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 x = r cos theta, y = r sin theta then prove that (del (x, y)) / (del (r, theta)) xx (del (r, theta)) / (del (x, y)) = 1

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 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 y=f(x+ct)+g(x-ct), then show that (del^(2)y)/(del t^(2))=c^(2)(del^(2)y)/(del x^(2))

If x = r cos theta, y = r sin theta, Find (del (x, y)) / (del (r, theta)), (del (r, theta)) / (del (x, y))

In any Delta ABC, prove that r.r_(1).r_(2).r_(3)=Delta^(2)

Compare Schrodinger equation with most important equation of Newtions law. (del^(2)psi)/(delx^(2))+(del^(2)psi)/(dely^(2))+(del^(2)psi)/(delz^(2))=-(E-V)(8pi^(2)m)/(h)psi " ""Schrodinger equation" ....(i) m(d^(2)x)/(dt^(2))=Fm " ""Newton's law"" "....(ii)

Prove that : (r_1)/(b c)+(r_2)/(c a)+(r_3)/(a b)=1/r-1/(2R)