Implicit Differentiation

The first differentiation should be

2x + y + xy' - 2yy' = 0

the second and third term are a result from the (fg)'= f 'g + g'f rule

After this the rest is quite straightforward.

There is  a slight error in the end result

It should be:

y' = (2x+y)/(2y-x)

x^2+xy-y^2=4

2x + y + xy' - 2yy'  = 0

y' (x - 2y)  =  -2x - y

y'  =  - [2x + y] /  [ x - 2y]   

y'  = [2x + y] / [ 2y - x]  

Thank you! I understand now.