e Is Truly the Natural Base
A three-step explainer showing why e is special: only for base e do the successive derivatives of an exponential stay the same.
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Free for classrooms, worksheets, slides and other non-commercial use under CC BY-NC 4.0, with credit to Ben Orlin.
Cartoon by Ben Orlin, Math with Bad Drawings. https://cartoons.mathwithbaddrawings.com/2018-08-17-e-is-truly-the-natural-base/ (CC BY-NC 4.0)Transcript
1. "Pick any point on an exponential curve." 2. "Compute successive derivatives at that point." (y → dy/dx → d²y/dx² → d³y/dx³ → ...)
3. "The results:" Base < e → derivatives go to 0 · Base > e → derivatives go to ∞ · Base = e → derivatives never change