Thank you!
Here is a way:
Manipulate[ ContourPlot[x^2 + y^2 + c x^2 y^2 == 1, {x, -2, 2}, {y, -2, 2}], {{c, 0}, -2, 10}] Solve[D[x^2 + y[x]^2 + c x^2 y[x]^2 == 1, x], y'[x]]