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

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

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

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

If u = log ((x ^(2) y + y ^(2) x)/(xy)) then x (del u)/( del x) + y (del u)/(del y)=

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=ax-by , 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= tan^(-1) ((x^(3) + y^(3))/(x-y)) , Prove that x(del u)/(del x) + y(del u)/(del y) = sin 2u .