How to predict time signal based on multi-input signals?

I would like to approximate the following relation by a neural network $y = \mathcal{f}(x_1(t),x_2(t))$ Here, I have only one output variable that is a function of 2 other variables which vary in time. Now, I want to be able to predict $y$ , given any shape of the 2 independent variables in time. For this reason, I have a training set corresponding to different input and output signals. However, I don't know how to make the neural network understand the concept of time which is very important since I expect the solution at time $t_k$ to be influenced by the previous instants in time. For this reason, I added as input variable the time derivative as $y = \mathcal{f}\left(x_1(t),x_2(t), \dfrac{\partial x_1 (t)}{\partial t}\right)$ This solution seems to work quite well for the fully connected neural network that I'm using. However, I would like to know if there are other ways to treat such problems where the time history is important.