Just a quick question regarding the units for a quantity. I just started reading a QFT textbook, and it starts out with a little bit of Calculus of Variations. Specifically, there is a result that says:
$$ \frac{\partial\langle T\rangle}{\partial x(t)} = -\frac{m\ddot{x}}{\tau}$$
where $\langle T \rangle$ is the average kinetic energy, $m$ is mass, and $x(t)$ is the path, with initial position at $t=0$ and final position at $t=\tau$. My question is that the units seem to be different on each side of this expression. It seems that on the left, there is units of $\frac{mass \times length}{time^2}$, and on the right there is $\frac{mass\times length}{time^3}$.
I know, a very nitpicky question haha. I'm sure this boils down to me not understanding the functional derivative as well as I should.
