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

Jun 22, 2015

As long as $x \ge 2$ the function boils down to $x - 2$ which has a derivative of $1$.
When $x \le 2$ the absolute brackets interfere, effectively turning the function into $2 - x$ which has a derivative of $- 1$
At the point $\left(2 , 0\right)$ the derivative could be either, depending on what side you approach it from.