# What is the derivative of sqrt(x^2-2x+1)?

Apr 30, 2015

This is a funny function:

$y = \sqrt{{x}^{2} - 2 x + 1} = \sqrt{{\left(x - 1\right)}^{2}} = \left\mid x - 1 \right\mid$.

So there are two functions and two derivatives:

${y}_{1} = x - 1$ for $x \ge 1$ and $y {'}_{1} = 1$

and

${y}_{2} = 1 - x$ for $x < 1$ and $y {'}_{2} = - 1$.

Its graph is:

graph{sqrt(x^2-2x+1) [-10, 10, -5, 5]}