You probably don't need to know how to compute a derivative, but there are tons of related concepts that are helpful for reasoning about systems in the world. You can always Google the chain rule, but having a general sense of the trend is often all you need.

For example, you don't have to remember how to derive it, but knowing that y'' = y is a positive feedback loop (exponential growth) but y'' = -y is a negative feedback loop (oscillating) is really useful in all sorts of common sense scenarios.

Learning is about concepts more than facts or algorithms.