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## Homework Statement

Find an equation of the tangent line to the curve xe^y+ye^x=1 at point (0,1).

## Homework Equations

I do not recall seeing the Implicit Function Theroem before, I even went back in my book (Stewart Calculus 6th) to check. I found this post but it does not help me understand the steps involved: https://www.physicsforums.com/showthread.php?t=79275

## The Attempt at a Solution

[tex]xe^{y}+ye^{x}=1[/tex]

[tex]\frac{d}{dx}(xe^{y})+\frac{d}{dx}(ye^{x})=\frac{d}{dx}(1)[/tex]

I am not sure if this requires the product rule but,

[tex]\frac{d}{dx}(xe^{y})=e^{y}+xe^{y}[/tex]

Then, I'm not sure on the other part???

[tex]\frac{d}{dx}(ye^{x})=y'e^{x}+ye^{x}[/tex]