Differential equation

Should I say I that I have good memory. I dont think so. I am real bad in maths. But, anyhow some strange equations keep flashing on my mind. It is the great differential equation(i guess).

Properties: A point is differentiable if it is continuous from that point to the left and from that point to right on a domain axis. If f is not continuous at a, we say f is discontinuous at a, or f has a discontinuity at a.

The Question:
1)Is it still differentiable at the same point after a time or
frequency shift?
2)Is it still differentiable if there is a jump on that point?
3)How if the funtion is no longer a function of two plain
variable of X and Y, but it is involving an arbitrary variable
of Z?

Fact: F(t) is obviously not differentiable at the instantenous of t.

At least I did not return all my maths to the lecture *wink*