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anonymous

  • 5 years ago

derivative of x^(e^x)

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  1. anonymous
    • 5 years ago
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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?

  2. anonymous
    • 5 years ago
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    yes thanks

  3. anonymous
    • 5 years ago
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    so would the answer be 1^(e^x) times e^x?

  4. anonymous
    • 5 years ago
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    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.

  5. anonymous
    • 5 years ago
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    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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