[" 11."x'y'z'=c," a constant,show that,at "x=y=z" ,"],[(del^(2)z)/(del x del y)=-(x log ex)^(-1)]

If x^(x)y^(y)z^(z)=c. Then show that x=y=z(del^(2)z)/(del x backslash del y)=-(x log ex)^(-1)

If z=f(x-cy) + F(x+cy) where f and F are any two functions and c is a constant, show that c^(2) (del^(2)z)/(del x^(2)) = (del^(2)z)/(del y^(2)) .

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

If u= y sin x then (del^(2)u)/(del x 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 u =tan^(-1)((x)/(y)) show that (del^(2)u)/(delxdely) = (del^(2)u)/(delydelx) .

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

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

Find del/(dely)((delz)/(delx)) if z=x^(y) + y^(x)