Hi guys,

Is it actually possible to derive the derivative of $\displaystyle e^x$ from first principles?

That is, to prove $\displaystyle \lim_{h \to 0}\frac{e^{x+h}-e^x}{h}=e^x$.

How do you go from there?

Or is it impossible because we actually define $\displaystyle e^x$ as a function whose derivative is $\displaystyle e^x$ itself?

Thanks.