homework and exercises - Geodesic equation from Euler - Lagrange

There are several ways to derive the geodesic equation. One of which is the variational method which I seemed to understand it because it was written in great details. Then it was mentioned that the geodesic equation can be derived from the Euler-lagrange equations only. I tried to pluh in the Lagrangian

$$L= \frac{1}{2} g_{\mu\nu}\frac{dx^\mu}{d\lambda}\frac{dx^\nu}{d\lambda}$$

in

$$\frac{d}{d\lambda}\frac{\partial L}{\partial(dx^\mu/d\lambda)} = \frac{\partial L}{\partial x^\mu}$$

but I am running into derivation problems and the corresponding chain rule. May you please help me out here, I have to understand how does the geodesic equation get derived from Euler-Lagrange equations. Thank you very much in advance!!