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Math Help - Differentiating exponential functions

  1. #1
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    Differentiating exponential functions

    I'm having trouble differentiating the function

    f(x)=axe^{(-bx)}

    where a and b are constants.

    I'm supposed to show that the turning point occurs at

    x=1/b

    Using the product rule I get

    a(e^{-bx})+(ax)(-be^{-bx})

    But no matter what I do with that, I can't seem to get

    x=1/b
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  2. #2
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    Quote Originally Posted by blackdragon190 View Post
    I'm having trouble differentiating the function

    f(x)=axe^{(-bx)}

    where a and b are constants.

    I'm supposed to show that the turning point occurs at

    x=1/b

    Using the product rule I get

    a(e^{-bx})+(ax)(-be^{-bx})

    But no matter what I do with that, I can't seem to get

    x=1/b
    a \cdot e^{-bx}-abx \cdot e^{-bx} = 0

    a \cdot e^{-bx}(1 - bx) = 0

    x = \frac{1}{b}
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  3. #3
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    Thank you
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