Derivative of Square Root Polynomial?

Question

How do you find the derivative of

$\sqrt{x^2 - 4x + 4}$

I applied Chain rule and got this

$\frac{x-2}{\sqrt{(x-2)^2}}$

However, the fill-in box requires two distinct functions (piecewise) where x > ______ and x < _____.

How would I get two equations from the derivative?

Problem Img

First you should write clearly what function you mean: $\sqrt{x^2-4x+4}$ or $\sqrt{x^2} - 4x +4$. Use: http://meta.math.stackexchange.com/questions/5020/mathjax-basic-tutorial-and-quick-reference — Karl, Nov 20 '14 at 08:17
Derivative of $\sqrt{x^2 - 4x + 4}$ is nothing but derivative of $|x-2|$ — Swapnil Tripathi, Nov 20 '14 at 08:20

score 1 · Accepted Answer · answered Nov 20 '14 at 08:20

1

Hint: $\sqrt{x^2-4x+4}=\sqrt{(x-2)^2}=|x-2|$

answered Nov 20 '14 at 08:20

gammatester

At x > 2, y = 1. At 2 > x, y = -1. I understand this part, but would I just plug them in for the piecewise function? – Sentient Nov 20 '14 at 08:23
Yes, and at $x=2$ your function has no derivative. But note the typo for your second case: it should be $x<2.$ – gammatester Nov 20 '14 at 08:24

1 Answers1