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Math Help - can u fin the derivative of this function

  1. #1
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    can u fin the derivative of this function

    i need the derivative of :
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  2. #2
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    Quote Originally Posted by geriniki View Post
    i need the derivative of :

    First simplify the power: \frac{1}{x}\left(x-\frac{1}{x}\right)=1-\frac{1}{x^2} , and now apply the chain rule to \left(e^{f(x)}\right)'=f'(x)\cdot e^{f(x)} ...

    Tonio
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  3. #3
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    The solution you provided doesn't match the problem.

    Can I ask what solution you arrived at?
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  4. #4
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    this must be solution it's in the textbook :/
    sorry i haven't written it correctly = x - 1/x isn't in the power
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  5. #5
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    Is this the correct function?

    f(x) = e^{1/x}\left(x-\frac{1}{x}\right)
    Last edited by drumist; January 24th 2010 at 03:50 AM.
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  6. #6
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    yes
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  7. #7
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    You may use the product rule:

    f'(x) = e^{1/x} \cdot \left(x-\frac{1}{x}\right)' + \left(e^{1/x}\right)' \cdot \left(x-\frac{1}{x}\right)

    Can you find the derivatives of x-\frac{1}{x} and e^{1/x}?
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  8. #8
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    yes thank you
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  9. #9
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    Do you see why Tonio was confused? (Because he never gives a wrong answer!)

    What you gave in your initial post was e^{\frac{1}{x}\left(x- \frac{1}{x}\right)} not e^{\frac{1}{x}}\left(x- \frac{1}{x}\right).
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