So this might be a really simple question but I am new to functionals.
I have a problem in which a path is described by $y(x)$. We are working with the action which is defined, in this case, as:
$$ S[y] = \int f(y,\dot y)dt$$
I am then asked to write the total derivative $\frac {df}{dt}$ in terms of the partial derivatives $\frac {\partial f}{\partial y}$ and $\frac {\partial f}{\partial \dot y}$
It is my understanding that $y$ and $\dot y$ are both functions of x. Wouldn't $\frac {df}{dt}$ simply be zero since $f(y,\dot y)$ has no explicit time dependence? Even if y is dependent in some way on $t$, I'm not sure how I would rewrite the partial derivatives to get a time derivative, especially when its not an explicit variable.