Find dx/dt when x=1, y=0 and dy/dt=2 for the equation x^2+2xy+y^2=1.

Question

I have
2xdx/dt + 2xdy/dt + 2ydy/dt + 2ydy/dt = 0
and -2 as my final answer. Is this correct?

Answer 1

If y = 0
2xdx/dt + 2xdy/dt = 0
if x = 1
dx/dt + dy/dt = 0
if dy/dt = 2
dx/dt + 2 = 0
dx/dt = -2
yes