- #1

- 833

- 30

But if now these functions are multivariate, and I have that ##h(x,y)=f(x)g(y)##, that is ##f(x,y)=f(x)## for all y, and similarly ##g(x,y)=g(y)## for all x. In this situation is also ensured the differentiability of ##h(x,y)## by the differentiability of ##f(x)## and ##g(y)##?