Question

If 3x^2+2xy+y^2=2 then the value of dy/dx at x=1 is

Answer 1

We have that
3x²+2xy+y²=2

find the derivative-------> (Implicit differentiation)
6x+2xdy/dx+2y+2ydy/dx=0 
collect dy/dx terms along one side 
dy/dx(2x+2y)= -6x-2y 
dy/dx= -2(3x+y)/2(x+y) = - (3x+y)/(x+y)

for x=1
dy/dx= -(3+y)/(1+y)= -(y+3)/(y+1)

the answer is
dy/dx=-(y+3)/(y+1)