Continuity vs Partial Derivatives vs Differentiability | My Favorite Multivariable Function

In single variable calculus, a differentiable function is necessarily continuous (and thus conversely a discontinuous function is not differentiable). In multivariable calculus, you might expect a similar relationship with partial derivatives and continuity, but it turns out this is not the case! In this example, what I call the cross function, we will see that both partial derivatives exist but that the function is nonetheless not continuous. This means our work is still cut out for us: we need to define a new concept to replace single variable differentiation in the multivariable context that is more than just partial derivatives existing. **************************************************** COURSE PLAYLISTS: ►CALCULUS I: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxfT9RMcRe ...