In the book Methods of Contemporary Gauge Theory by Yuri Makeenko, the loop equation in the large-$N$ limit is given by
$$\partial^x_\mu \frac{\delta}{\delta \sigma_{\mu \nu}} W(C) = \lambda \oint_C dy_\nu \; \delta^{(d)}(x-y)W(C_{yx})W(C_{xy}). \tag{12.59}$$
Equation (12.59) in the book, page 264. Where $\frac{\delta}{\delta \sigma_{\mu \nu}}$ is the area derivative and $W(C)$ is the expectation value of a closed wilson loop.
I am trying to understand this equation by evaluating an explicit example, but I couldn't find any case that I was able to evaluate (mostly because I don't understand the equation and how to apply the definitions, like the area derivative to the Wilson loop, the book doesn't have a particular case explaining these things).
For example, if we consider a circular Wilson loop with radius $R$ and expectation value given by $e^{R^2}$. I would like to know how do I take the area derivative of this and what $W(C_{xy})W(C_{yx})$ would correspond to in this case. Or maybe other example that could help me understand those abstract concepts.
