A more global viewpoint of the concept of differentiability is when a whole function is differentiable everywhere. In this case, we can define a mapping assigning each point to the limit of the difference quotient at this point. This map is called the derivative of a function. It is then of interest how operations on functions like multiplications, additions, quotients, compositions, etc behave under computing the derivative. It turns out that one can show certain rules of differentiation, which are also touched upon in this episode.

Picture from Nick Youngson CC BY-SA 3.0 Alpha Stock Images