Question

Question is in the attachment. Please help.

Answer 1

@eliassaab

Answer 2

you can use the fundamental theorem of calculus

Answer 3

if you take the derivative of that integral

Answer 4

Which calculus?? Integral? We have to prove differentiability

Answer 5

I don't have a book which has this kind of problems, if anyone has, do tell me the name. It should covers topics of limit, continuity, differentiability from R^2->R and must contain examples of mappings from R^m->R^n

Answer 6

I got the answer finally. Here del f/del x=g(x+y)=del f/del y. Since it ia given that g is continuous, we have the first order partial derivatives are continuous, and hence by the sufficient condition of differentiability, we can conclude that f is differentiable