Question

derivative of x^(e^x)

Answer 1

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?

Answer 2

yes thanks

Answer 3

so would the answer be 1^(e^x) times e^x?

Answer 4

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.

Answer 5

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.