Since the derivative of x^-1 is -x^-2, is it correct to then work it further to get the "best answer" as
1/-sqrt x
and then rationalize the denominator by multiplying by 1 as in
(1/-sqrt x) * (-Sqrt x/-Sqrt X)
to get
-Sqrt x / x ???

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that probably depends on your teacher? Rationalizing it is certainly not incorrect.

My instructor counts off for math grammar I never heard of before.

ask him/her then to be sure. In my class I could leave it as x^-1

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