This isn't quite the same as the rule above. Suppose . Then:
In physics (or anything else where the symbols can have units and aren't just pure numbers), this is not generally true unless the arguments are dimensionless. In fact this is a specific example of a general rule that one cannot substitute equalities that carry units into any functional form that has a power-series expansion. On the other hand one can substitute in quantities that in some sense ``look the same'' that are dimensionless. This is easy to understand. Supposed I know that is a length in meters. I can certainly write down its exponential: . But does this make sense?
If I expand in its well-known power series (summarized, derived,
The only way this can make sense is if we write something like: