How Do You Apply Implicit Differentiation Correctly?

[JessicaJ283782]

Homework Statement

Find the derivative of:

x+xy=y^2

Homework Equations

So I know you have to differentiate it, and it would be:

1+xyy'=2yy'

The Attempt at a Solution

Moving the terms with y' to one side:
1+xyy'-2yy'=0

xyy'-2yy'=-1

Factoring out y'

y'(xy-2y)=-1

y'=-1/(xy-2y)

Did I do that correctly?

 

[Panphobia]

The derivative of xy is not xyy' but it is y + xy'

 

[TheRedDevil18]

For the xy part, you should use the product rule, f'g+g'f