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Thread: Differentiation Problem

  1. #1
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    Differentiation Problem

    I have an engineering application, that amounts to a differentiation problem that has me stumped.

    If $\displaystyle q=\frac{1}{\alpha^2}-(\frac{t}{\alpha}+\frac{1}{\alpha^2})e^{-\alpha t}$

    Find $\displaystyle \frac{dq}{dt}$.

    I came up with $\displaystyle -\frac{t}{e^{\alpha t}}$ and several other versions, but I know that I'm off.

    Can anyone put me on track?
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  2. #2
    MHF Contributor matheagle's Avatar
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    Quote Originally Posted by kaiser0792 View Post
    I have an engineering application, that amounts to a differentiation problem that has me stumped.

    If $\displaystyle q=\frac{1}{\alpha^2}-(\frac{t}{\alpha}+\frac{1}{\alpha^2})e^{-\alpha t}$

    Find $\displaystyle \frac{dq}{dt}$.

    I came up with $\displaystyle -\frac{t}{e^{\alpha t}}$ and several other versions, but I know that I'm off.

    Can anyone put me on track?

    I get $\displaystyle te^{-\alpha t}$
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  3. #3
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    $\displaystyle q=\frac{1}{\alpha^2}-\left(\frac{t}{\alpha}+\frac{1}{\alpha^2}\right)e^ {-\alpha t}$

    $\displaystyle \frac{dq}{dt} = -\left(\frac{t}{\alpha}+\frac{1}{\alpha^2}\right) \left( -\alpha e^{-\alpha t} \right) - \frac{1}{\alpha} e^{-\alpha t}$

    $\displaystyle = t e^{-\alpha t} + \frac{1}{\alpha} e^{-\alpha t} - \frac{1}{\alpha} e^{-\alpha t}$

    $\displaystyle = t e^{-\alpha t}$
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