Also, it is very bad practiice to write a series of "=" for things that are not actually equal! The very first line in your chain:
is, in fact equal to y. Everything after that is equal to its derivative. The very next line should be
and after that it would be alright to just write "= ".
While using the quotient rule works, personally, I would have used the product rule from the original form.
Indeed, the preference is almost unavoidable when the denominator is a power of other than one - because then squaring produces a denominator that usually calls for simplifying later, whereas the product rule heads straight for the simpler version.
Just in case a picture helps...
... where (key in spoiler) ...
Spoiler:
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Don't integrate - balloontegrate!
Balloon Calculus; standard integrals, derivatives and methods
Balloon Calculus Drawing with LaTeX and Asymptote!