Question

How do you find the derivative of `abs(x-2)`?

Answer 1

Actually there are two derivatives.

Explanation:

As long as `x>=2` the function boils down to `x-2` which has a derivative of `1`.

When `x<=2` the absolute brackets interfere, effectively turning the function into `2-x` which has a derivative of `-1`

At the point `(2,0)` the derivative could be either, depending on what side you approach it from.
graph{|x-2| [-7, 13, -2.4, 7.6]}