Given

$\displaystyle L=L(x,y,z,\dot x,\dot y,\dot z) $

then I can write the six partial derivatives (as I would when forming Euler-Lagrange equations):

$\displaystyle \frac{\partial L}{\partial x^\mu}$, $\displaystyle \frac{\partial L}{\partial \dot x^\mu}$

or I can write the three partial derivatives

$\displaystyle \partial_\mu L=\frac{\partial L}{\partial x^\mu}=\frac{\partial L}{\partial x^\mu}+\frac{\partial L}{\partial \dot x^\mu}\frac{\partial \dot x^\mu}{\partial x^\mu}$

These two options use the same notation but give different things. How am I to know which is required? Does the $\displaystyle \partial_\mu$ notation mean that the derivatives are of the second kind?