Question 1044352
The tangent line at the point (0,0) will NOT exist, as the derivative at (0,0) doesn't exist there.  
Although the point (0,0) is a point on the curve, the relation is not differentiable at that point.

Using implicit differentiation,

{{{1/(x+1) + e^(x+y^2)*(1+2y*(dy/dx)) = 0}}}.

Substituting the coordinates of (0,0) into this differential equation would give

{{{1/(0+1) + e^(0+0^2)*(1+2*0*(dy/dx)) = 1 + e^0*1 = 2 <> 0}}}.