Implicit Derivative (no calculator)

Question

4x² + 2xy + y² = 12

Could someone explain what the steps/rules used for each step are rather than provide the answer? Thank you!

Answer 1

4x^2 +2xy+y^2=12

8x+2xy'+2y +2yy' =0

use power rule and product rule

4x+xy' +y+yy'=0

isolate y'

(x+y)y'=-4x-y

y'=dy/dx= -(4x+y)/(x+y)

y=-x+/-sqr(-3x^2 +c)

or graph the ellipse

(.5, 0), (-.5, 0) = x intercepts with c=1