I was reading about Lagrangian mechanics on Wikipedia (https://en.wikipedia.org/wiki/Lagrangian_mechanics) and came across the equation for motion in the "Pendulum on a movable support" section and haven't been able to figure out where the $\dot{\theta}$ in the derivative for ${x_{pend}}$ came from. Intuitively, it makes sense that there is an angular velocity $\dot{\theta}$ term but I don't know how to derive it. The equation from the article is replicated below $${x_{pend}} = x + l \, sin\,\theta \quad \Rightarrow \quad \dot{x}_{pend} = \dot{x} + l\dot{\theta}\,cos\,\theta$$
Thank you.
The key is to regard $\theta$ as a function of time. Then the second term is just an application of the chain rule $$\frac{\delta}{\delta t}\sin(\theta(t))=\dot\theta(t)cos(\theta(t))$$