technically yes, technically no. it would depend on whether we are considering negative x's or positive or both. remember,
it is better not to simplify in this case, so there is no ambiguities. just apply the chain rule, as you so rightly directed, and call it a day
After I substituted in for x, and used the definition of the derivative of a function to set the rest of the problem up, how would I get out of the denominator?
I used the conjugate method, then I got a common denominator. I just simplified from there on out. Is this not right?