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

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Answer 1 · 2015-06-22T20:36:29

Actually there are two derivatives.

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

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

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

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