What is the derivative of e^x? Why?

Question

anonymous · Answer

depends on what your definition of $e^x$ is

anonymous · Answer

one definition is that $e$ is the number that makes 
$$\lim_{h\to 0}\frac{e^h-1}{h}=1$$ true

anonymous · Answer

the answer to the first question is that the derivative of $e^x$ is $e^x$ but the "why" depends entirely on how you define the function $e^x$

anonymous · Answer

Oh I see. Thank you so much! I remember learning that the derivative of e^x is e^x and I was just confused as to why.

anonymous · Answer

@satellite73 this was also confusing to me. is there a mathematical proof involved?

anonymous · Answer

https://www.khanacademy.org/math/calculus/differential-calculus/der_common_functions/v/proof--d-dx-e-x----e-x i tried searching this on google. this video will probably help @iGunwoo

anonymous · Answer

Ah. This website as well as KhanAcademy are my saviors, haha. Thanks a lot! @jolee

anonymous · Answer

at the risk of repeating myself, you cannot show that the derivative of $e^x$ is $e^x$ without having a precise definition of $e^x$ or at the very least of $e$

anonymous · Answer

much as i like khan, this video assumes facts not in evidence, as they say on perry mason