Consider the real function f(x,y)=xy(x2+y2)-N,in the respective cases N = 2,1, and 1/2. Show that in each case the function is differentiable (C[tex]\omega[/tex]) with respect to x, for any fixed y-value. whats the strategy for proving C[tex]\omega[/tex]-differentiability here? i have to show with induction that f is still continuos after n+1 derivatives with respect to x, or am i wrong? seems like, one has to look after a pattern in the continued derivatives of f, for write down the (n+1)nth derivative. on the other hand, one might have the differential quotient in mind, taking the limit, meeting a boundary condition(in the complex domain the radius of convergence), but i could only think of the 1th derivative here.