Assuming y is a function of x and you want to differentiate with respect to x, then the product rule yes, but also the chain rule because arctan y is a composite function where y is the inner function of x.

Just in case a picture helps...

... where (key in spoiler) ...

Spoiler:

Pauls Online Notes : Calculus I

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Don't integrate - balloontegrate!

Balloon Calculus; standard integrals, derivatives and methods

Balloon Calculus Drawing with LaTeX and Asymptote!