Derivative of e^x from the first principle

[Vibaravi]

Mr Tambuwal, thank you for proving the derivative of e^x by first principles without using circular reasoning like many videos do. Most other videos prove this using L’Hospitals’ rule or Taylor expansion which doesn’t make sense from a logic point as they are assuming the thing they are trying to prove. Please continue your amazing work :)

[fizisistguy]

By far the most logical and simple proof. Thanks so much, the other proofs use l'hopital's rule without acknowledging that we shouldn't really be using an advanced tool to prove a very basic thing, but rather the opposite.

[quixata]

This can be shown easily. Lim (h->0) (e^h - 1)/h is 1 can be showed by expanding e^h = 1 + h + h^2/2! + ...
so that e^h - 1 = h + h^2/2! + h^3/3! + .... and hence (e^h - 1)/h = 1 + h/2! + h^2/3! + .... and consequently the limiting value of this expression when h -> 0 is 1 as the rest of the terms go to 0.

[sriprasadjoshi]

tambuwal, thank you for considering my comment

[YualChiek]

Great job! You deserve a lot more subscribers.