Question

I watched the Unit 1, Session 17 clip explaining why e is in fact "the most natural logarithmic function" but I still don't understand why or how it is... I don't know why it's just not clicking for me, I've read the notes for the clip and I still don't understand why/how it's more natural than any other base?

Answer 1

The derivative of e^x is "simpler" than the derivative of b^x where b is any other base.
So maybe that is enough to claim e is "more natural"

But "e" crops up in the most amazing way, and seems very special. See
http://www.khanacademy.org/math/algebra2/exponential_and_logarithmic_func/continuous_compounding/v/introduction-to-compound-interest-and-e

and
http://www.khanacademy.org/math/integral-calculus/sequences_series_approx_calc/maclaurin_taylor/v/euler-s-formula-and-euler-s-identity