Derivative question, can someone explain it to me?

Question

Differentiate tan(x-y)= y/((x^2)-2). Do not solve for y'

Answer 1

Differentiate tan(x-y)= y/((x^2)-2)

I assume we differentiate each side of the equation (implicit differentiation), & not solve for y'

sec²(x-y) • (1-y') = [(x²-2)y' - y(2x)] / (x²-2)²

Then we simplify and solve for y'.