Excuse my ignorance .. my math is rusty very rusty

Playing with the graphing calculator I put together the equation ; X( square root of X squared ). The graph looked interesting so I took it's derivative by hand and after fumbling it up a few times I worked out and justified the same derivative as the calculator ; f'(x) = 2 * absolute value of X.

The question I have is that when I change the form of the original function to ; X( absolute value of X) .. replacing the the square root of x squared with absolute value of X which should be equivalent ?? .. I can't seem to get the same derivative back again as an answer. I get instead absX + X.

Could it be simply based on the definition of square root of x ? I can only think that the derivative of the absolute value of X would be 1. Simple enough but applying the product rule to X(abs of X) leaves me with absX + X. Does the defintion of square root of X dictate that X in this case must be the abs of X and so add to equal 2(abs of X ) ?