How do I find this tangent line?

Calculus Level 4

Let \( y = y(x) \) be the function implicitly determined by the equation \[ x^2 +2xy + 3 \ln{y} = e^y .\]

Find the angular coefficient of the line tangent to \( y(x) \) on \( y = 1 \), located at the first quadrant of the Cartesian plane.

Give your answer to 1 decimal place.

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