How do you prove on the basis of the definition, the function f defined by f(x,y)=xy(x+y) is differentiable at every point of its domain?

My definition goes:  If the function has its derivatives at point (a,b) then the function is differentible at (a,b)

How do you prove on the basis of the definition, the function f defined by f(x,y)=xy(x+y) is differentiable at every point of its domain?