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

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Answer 1 · 2015-04-30T15:01:33

This is a funny function:

#y=sqrt(x^2-2x+1)=sqrt((x-1)^2)=abs(x-1)#.

So there are two functions and two derivatives:

#y_1=x-1# for #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]}