Partial Differentiation in Polar?

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$$ r = e^{\theta} $$

This is the equation of a polar curve, I need to find $dy/dx$ of the curve in Cartesian. My approach was to express the above equation in terms of $x$, $y$ and $\theta$:

$$ x^2 + y^2 = e^{2\theta}$$

But I am confused because how do I deal with the $\theta$? It is a variable and is dependent on both $x$ and $y$. My first thought was to use partial derivatives in an attempt to make $\theta$ a constant but I don't really have an experience with them. Any tips?