Question

1. is the derivative of the function f(x)=5e^(4x-9z) f'(x)= -25e^(4x-9z)?

2. Is the derivative of the function f(x)=e^(2x)-e^(-2x) f'(x)=2e^(2x)+2e^(-2x)?

3. If f(x)=e^-x^-1, would f'(2)=-1/4e^(1/4)?

Answer 1

1) if you have a function f(x) , what is that 9z doing there in the exponent?

2) yes

3.) is that a stair-case exponent or is it
f(x) = (e^x)^-1 ?
= e^-x ?
on the other hand, Wolfram read your equation as
y = e^(1/x)

http://www.wolframalpha.com/input/?i=plot+y+%3D+e%5Ex%5E-1

in that case,
dy/dx = (-1/x^2) e^(1/x)
when x = 2
dy/dx = (-1/4)e^(1/2)
or -(1/4) √e

Answer 2

1.)sorry i meant to put x not z. so 9x.

3.)yes it is a stair case exponent

Answer 3

1) in that case why not just write the exponent as -5x ?
y = 5 e^(-5x)
y' = -25 e^(-5x)

3. but your answer resembles the other interpretation, for which I gave you a solution.
I stand by that answer.