What is the derivative of $\sqrt{x^{2} - 2 x + 1}$ $sqrt(x^2-2x+1)$ ?

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Answer 1 · 2015-04-30T15:01:33

This is a funny function:

$y = \sqrt{x^{2} - 2 x + 1} = \sqrt{{(x - 1)}^{2}} = | x - 1 |$ $y=sqrt(x^2-2x+1)=sqrt((x-1)^2)=abs(x-1)$ .

So there are two functions and two derivatives:

$y_{1} = x - 1$ $y_1=x-1$ for $x \geq 1$ $x>=1$ 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]}

What is the derivative of sqrt(x^2-2x+1)√x2−2x+1sqrt(x^2-2x+1)?