I think that you are just a little bit confused on this one. The derivative of e^x is e^x, but that is because you are differentiating a variable exponent. There are a lot of derivatives associated with logarithmic and exponential functions.

The derivative of e^2 would be 2e because the exponent was a constant and you could use the x^n = nx^(n-1) rule. This rule is used when a variable is raised to a constant power. Play close attention to what the variable is in the equation. Look around the internet for rules for differentiation of logarithmic functions and you will see where you went wrong.