[" Q30.Verify that "(del^(2)u)/(del x del y)=(del^(2)u)/(del y del x)," when u is "],[[" (i) "sin^(-1)(x)/(y)]]

If u=x^2+3xy+y^2 Verify (del^2u)/(delxdely)=(del^2u)/(delydelx) .

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

If u=x^y then find (del u)/(del x) and (del u)/(del y) .

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

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

If u =x ^(3) +2xy^(2) -x ^(2)y show that (del^(2)u)/(delxdely) =(del^(2)u)/(delydelx).

If f = x ^(3) + y ^(3) + 3x ^(2) y ^(2) + 4 x ^(2) y find (del f)/( del x ), ( del f )/(del y), (del^(2) f )/( del x del y ), (del ^(2) f )/( del y del x) , (del ^(2) f)/( del x ^(2)), (del ^(2) f)/( del y ^(2)).

If u= x^3-3xy^2 , show that (del^2u)/(delx^2)+(del^2u)/(dely^2) =0

If u=f(y/x) , then x(del u)/(del x) + y(del u)/(del y) =_________

If u=ax-by , then ((del u)/(del y))=