# Uncertainty propagation

I am having an issue solving the following problem. I am propagating the uncertainty of some input parameters through a mathematical model represented by $u$ to determine the uncertainty on an output function. The propagation I use can be found on the picture. The problem is that the variable $u$ is also function of time $t$ besides $A_i$, $\omega_i$ and $k_i$. Any suggestions how to handle this? thanks is advance for your help!