Find the derivitive of the function? Help

[ForeverMo]

Find the derivative of the function? Help:)

Homework Statement

g(x)=√x^2-2x+1

Homework Equations

The Attempt at a Solution

I rewrote the problem as g(x)=(x^2-2x+1)^1/2
Then..
1/2(x^2-2x+1)^-1/2(2x-2)(2)
But I got it wrong at that step whenever I wrote the "2"
Can you help?

 

[Mark44]

Homework Statement

g(x)=√x^2-2x+1

Homework Equations

The Attempt at a Solution

I rewrote the problem as g(x)=(x^2-2x+1)^1/2
Then..
1/2(x^2-2x+1)^-1/2(2x-2)(2)
But I got it wrong at that step whenever I wrote the "2"
Can you help?

You don't need that final 2. What you have is u^1/2, where u = x² - 2x + 1.
d/dx(u^1/2) = (1/2)u^-1/2 * du/dx

 

[ForeverMo]

Ok, I understand.. But for some reason I was wanting to write the derivitave of 2x, which is 2 right??

 

[Mark44]

du/dx = 2x - 2

 

[ForeverMo]

Ohhhh ohk I knew that..Thanks a lot :D
Could you please take a look at my other post?

 

[HallsofIvy]

Actually, $y= (x^2- 2x+ 1)^{1/2}= ((x- 1)^2)^{1/2}= |x- 1|$
That has derivative -1 if x< 1, 1 if x> 1 and is not differentiable at x= 1.

That is the same as $y'= (1/2)(x^2- x+ 1)^{-1/2}(2x- 2)= (x-1)/|x- 1|$.