Analyzing the differentiability of $\sqrt{x^2}$

Analyzing differentiability of $\sqrt{x^2}$

As we see a quick simplification of $\sqrt{x^2}$ yields $x$ which is a straight line.
Another simplification yields $|x|$

Clearly $|x|$ is not differentiable whereas $x$ is differentiable.

Some people might contest the $|x|$ simplification saying that is not true. I think both simplifications are correct and hence depending upon the simplification this may or may not be differentiable.

RP
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