Consider the graph of x^2+xy+y^2=1. Use implicit differentiation to find all points on the graph where the tangent line is parallel to the line y=-x.

Where do I go after I implicitly differentiate this thing?

2x+y'+2y*y'=0

y'+2y*y'=-2x

y'(1+2y)=-2x

y'=-(2x)/(1+2y)

Did I do that right?