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Math Help - Basic derivative, understanding a question.

  1. #1
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    Basic derivative, understanding a question.

    Hey,

    The derivative of  t e^3 is  e^3 . I do not understand why. The answer in my text says that the t is a constant. However, I do not understand how to tell when something is a constant, and when something is not.

    Originally in this problem I used the chain rule, and found the solution to be
     (1)(e^3) + (t)(e^3)
     = e^3 + t e^3
    which is not the answer.

    I am looking for an explanation, in plain english please.

    Thank you!
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  2. #2
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    Quote Originally Posted by Kakariki View Post
    Hey,

    The derivative of  t e^3 is  e^3 . I do not understand why. The answer in my text says that the t is a constant. However, I do not understand how to tell when something is a constant, and when something is not.

    Originally in this problem I used the chain rule, and found the solution to be
     (1)(e^3) + (t)(e^3)
     = e^3 + t e^3
    which is not the answer.

    I am looking for an explanation, in plain english please.

    Thank you!
    Actually, e^3 is a constant. t is a variable.

    So \frac{d}{dx}(e^3 t) = \frac{d}{dx}(e^3 t^1)

     = 1e^3 t^0

     = e^3.
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  3. #3
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    Quote Originally Posted by Kakariki View Post
    Hey,

    The derivative of  t e^3 is  e^3 . I do not understand why. The answer in my text says that the t is a constant. However, I do not understand how to tell when something is a constant, and when something is not.

    Originally in this problem I used the chain rule, and found the solution to be
     (1)(e^3) + (t)(e^3)
     = e^3 + t e^3
    which is not the answer.

    I am looking for an explanation, in plain english please.

    Thank you!
    t is not the constant. e^3 is the constant. Remember, e is just a number (constant, not a variable). Any constant cubed will also be a constant.

    Just as the derivative of 4t will be 4: the derivative of e^3t will be e^3.

    Does that help?

    Mathemagister
    Last edited by mathemagister; March 30th 2010 at 01:40 AM. Reason: latex
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  4. #4
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    OH!!!!!!!!!! That makes complete sense. I was under the impression that t would be a constant, and it just didn't make any sense to me at all. e^3 being a constant does make sense though! The graph of te^3 would be a line, would it not? Then the derivative would be e^3 (a horizontal line).

    Wow, I was just looking at it wrong.

    THANK YOU!
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