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

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

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

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

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

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

If U=(y)/(z)+(z)/(x), then find x(del u)/(del x)+y(del u)/(del y)+z(del u)/(del z) .

If u=(x-y)^(4) + (y-z)^(4) + (z-x)^(4) then sum (del u)/(del x)=

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