Combine implicit, inverse-circular and integral methods
Treat y as a differentiable function of x near the specified point. Construct the displayed derivative and tangent templates; verify the point before differentiating
\[e^{3(x-(0))}+2(x-(0))y+3(y-(-2))=1,\qquad (x,y)=(0,-2)\]
\[y'=\frac{Ae^{3(x-(0))}+By}{Cx+D},\qquad y=mx+q\ \text{(tangent)}\]