Derivative of a lemniscate at the left hand side How does $${d \over{dx}}(3(x^2+y^2)^2)$$ turn into $$12y(x^2+y^2){{dy} \over{dx}}+12x(x^2+y^2)$$? I'm having a hard time solving it algebraically without it turning into a huge polynomial.

Thank you Sky, I see now that upon one part of the chair rule becoming a complete polynomial with a coefficient it can then be distributed amongst the single variables of ydy/dx and x respectively without having to foil as if it were (2x+2x)(x^2+y^2).
