I hava function $F(X,Y)$.
$X(t)$ and $Y(t)$ : both are functions of a third variable $t$.
In addition $X(Y(t), t)$: $X$ is a function of $Y$, which is a function of $t$, and $t$.
The third point is strange but this is a theoretical model, there are no actual functions to substitute in (in particular I cannot substitute $Y(t)$ simply with a polynomial of $t$ or the functional form).
I need to calculate $dF/dt$ : the partial derivative of the function with respect to $t$.
My solution:
$$ \frac{dF}{dt} = \frac{dF}{dX} \left( \frac{dX}{dY} \times \frac{dY}{dt} + \frac{dX}{dt} \right) + \frac{dF}{dY} \times \frac{dY}{dt} $$
($\times$ are product signs)
Do you think it is correct?
Thank you for your time.
