Question

Find y prime if arctan(xy) = 1 + (x^2*y)

Answer 1

I'm pretty sure that these tips which I give you will make you able to sort things out.
According to the fact that derivative of the function f(x) = y, you an use these formulae in order to calculate the needed result : $arctan(xy) = 1+ x^2*y =\ \textgreater \ xy = tan(1+x^2y)$
$y + xy' = sec^2(1+x^2y)(2x*y + y'*x^2)$
Do hope this will lead you to the corect answer! Regards.