Evaluate `(delz)/(delx)` and `(delz)/(dely)`, if
`z=x^2y-xsin(xy)`

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

Find (dy)/(dx) , when: xsin2y=ycos2x

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)

For conservative force field, vec(F)=-(delU)/(delx)hat(i)-(delU)/(dy)hat(j)-(delU)/(delz)hat(k) where Frarr Maginitude of Force. Urarr Potential energy and (delU)/(delx)= Differentiation of U w.r.t. x keeping y and z constant and so on. Choose incorrect matching :-

If x+2y+3z=0 and x^3+4y^3+9z^3=18xyz then evaluate (x+2y)^2/(xy)+(2y+3z)^2/(yz)+(3z+x)^2/(zx)

Find x and y when (7x-2y)/(xy)=5,(8x+7y)/(xy)=15

If x=1, y=2, z=-1 then find the value of z^2-2xy(x-y)

If x + y + z = 0 , then the value of (x^2)/(yz) + (y^2)/(zx) + (z^2)/(xy) is: