What is the derivative of x^2 -4y -tanxy=0

Answer 1

Do it implicitly.
Your first line derivative is
2x - 4dy/dx - sec^2 (xy)(xdy/dx + y) = 0

expand the term at the end
keep terms containing dy/dx on the left side, take everything else to the right.
factor out the dy/dx, and isolate it.