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Math Help - Derivatives of Functions

  1. #1
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    Derivatives of Functions

    The question is asking to find the derivative of the function:

    y=4-7e^-x^9

    I am confused because there are so many exponents. It would really help to see the work with the answer.
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  2. #2
    MHF Contributor Siron's Avatar
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    Re: Derivatives of Functions

    You have to be clearer.
    Is it:
    y=4-7e^{(-x^9)}? ...
    If yes, use the chain rule.
    The derivative of e^u=e^u.D(u)
    Let u=-x^9
    Last edited by Siron; July 13th 2011 at 07:52 AM.
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  3. #3
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    Re: Derivatives of Functions

    Quote Originally Posted by StarDancer19 View Post
    The question is asking to find the derivative of the function:

    y=4-7e^-x^9

    I am confused because there are so many exponents. It would really help to see the work with the answer.
    It would really help if you put in parentheses so we knew if you meant 4-7e^{-x^9} or 4-7(e^{-x})^9 or something else.

    CB
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  4. #4
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    Re: Derivatives of Functions

    Sorry about the clearness. It is: 4- [7e^(-x^9)]

    I understand how to use the chain rule to find that u=-x^9

    What I need help on is actually seeing the work of the rest
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  5. #5
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    Re: Derivatives of Functions

    Sorry about that, but the question I am asking is the first suggestion you had.
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  6. #6
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    Re: Derivatives of Functions

    \dfrac{d}{dx}f[g(x)] = f'[g(x)] \times g'(x)

    In your example you have f(x) = -7e^{g(x)} \text{  and  } g(x) = -x^9

    ======================================

    Alternatively:

    \dfrac{dy}{dx} = \dfrac{dy}{du} \cdot \dfrac{du}{dx}

    You have y(u) = -7e^u \text{  and  } u(x) = -x^9

    ======================================

    Both notations depict the chain rule so pick whichever is easier to understand
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  7. #7
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    Re: Derivatives of Functions

    Quote Originally Posted by StarDancer19 View Post
    Sorry about the clearness. It is: 4- [7e^(-x^9)]

    I understand how to use the chain rule to find that u=-x^9

    That I need help on is actually seeing the work of the rest
    What that tells me is that you have no idea how to use the chain rule!
    You don't use the chain rule to "find that u= -x^9".

    If u= -x^9 then f(x)= 4- 7e^{-x^9} becomes f(u)= 4-7e^u. Can you find df/du?

    And what is du/dx?

    The chain rule says \frac{df}{dx}= \frac{df}{du}\frac{du}{dx}.
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