some math help

[nanotech fur]

alright i know that the derivative of e^x=e^x but i can't derive it without having prior knowledge of is derivative

this is far above my teaching in mathematics and isn't required anything but i don't like memorizing rules without knowing the logic behind them

d/dx e^x=( e^(x+d) - e^(x))**\**d

we start here obviously but how do we move from here?

d/dx ln(x)=x'/x

is confusing as well could someone help with that.

if you don't think you know the right answer just tell me what you would do... curling up in the corner and crying is a reasonable response.

[kalleguld]

Um, if I understand this question correctly you want proof that d/dx e^x = e^x and d/dx lnx = 1/x
Is that correct? if so, i'd like to try to help you, but I can't guarantee anything, i don't have my books anymore.