If u= y sin x then `(del^(2)u)/(del x del y)`=___________

If u=y^(x) , then (del u)/(del y) =__________

If u is a homogenous function of x and y of degree n, then x(del^(2)u)/(del x^(2)) + y(del^(2)u)/(del x del y) = __________ (del u)/(del x) .

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

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

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

If w(x,y) = xy + sin(xy) , then prove that (del^(2) w)/(del y del x) = (del^(2) w)/(del x del y)

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

If u (x,y) = (x ^(2))/( y)- (2y ^(2))/(x) then (del^(2) u)/(del x dely) - (del ^(2) u)/(dely delx) is :

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