She is derivation, a transform of functions that describes rate of 𝑓(𝑥) changing as 𝑥 changes. (This can be represented visually as the slope of the graph 𝑦 = 𝑓 (𝑥).) He is the exponential function 𝑒^𝑥^, which is the only* non-zero function whose derivative is itself - in other words, unaffected by derivation. The number 𝑒 is a constant (around 2.718) and the base of natural logarithms, hence the title.

* except its multiples such as −2 𝑒^𝑥^, which are... just... uh... derivative works