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derivative of x^(e^x)

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This is just a chain rule problem. What was done to x first? e^x. That's the "inside" function. X raised to that power is the "outside" function. Now just apply the chain rule, working from "outside" to "inside." Does that give you enough?
yes thanks
so would the answer be 1^(e^x) times e^x?

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Other answers:

No. You've mishandled the first derivative. Since it's x raised to a power, you must begin by using the derivative rule that would apply to x^2, x^5, x^99, etc. That result times e^x will be correct.
Agghhh. My last post didn't post. My answer above is not correct. Because x is raised to a power that also includes x, this is much more complicated than I originally thought. My TI-89 can't do it at all. I have an answer, but am not sure of it. I can tell you how I started if you're interested.

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