While the conventional "existence of a limit" in 1D is nice (and as a nice side effect gives us the derivative expression too), the general definition is more powerful and it is useful to contrast …

Differentiability refers to the existence of a derivative while differentiation is the process of taking the derivative. It is like the difference between perceptibility and perception.

Differentiability means that the function has a derivative at a point. Continuity means that the limit from both sides of a value is equal to the function's value at that point.

How does one prove differentiability? Ask Question Asked 10 years ago Modified 10 years ago

The reason Rolle's theorem talks about differentiabilty on the open interval $ (a,b)$ is that it is a weaker assumption than requiring differentiability on $ [a,b]$. Normally, theorems might try to …

Jul 20, 2019 · Thanks for this answer. Would you happen to have a resource that would help me practise using this definition? and proving differentiability of functions of two variables?

Why does differentiability imply continuity, but continuity does not mean differentiability? I am more interested in the part about a continuous function not being differentiable. All I could find

Jan 18, 2017 · Lipschitz continuity implies differentiability almost everywhere. Ask Question Asked 8 years, 9 months ago Modified 4 years, 1 month ago

Ok, so in my notes it says Prop 1: If a function is differentiable, it will be continuous AND it will also have partial derivatives. Prop 2: If a function is continuous, or has partial derivative...

Dec 11, 2024 · How does the above definition of differentiability fit into this framework? I think it is the definition of Gateaux differentiability simplified for two variable functions but I'm not sure. …