first derivative of e^-x

You are confused because your concept is not clear and using the derivative formula of x^n into the wrong place
d/dx (x^n)=nx^(n-1) and notice that the base x is the variable !!
However e is a natural number (constant), so the previous formula does not hold !
The correct derivative formula of a^x is (a^x)lna and for a=e, the formula becomes f'(e^x)=e^x
Using chain rule f'(e^(-x))=d/d(-x)[e^(-x)]d(-x)/dx=-e^(-x)

e is the natural number.

d/dx (e^x) = e^x

By chain rule,
d/dx (e^-x)
= d/d(-x) (e^-x) * d/dx (-x)
= (e^-x) * (-1)
= - e^-x