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Math Help - Can't find derivative.

  1. #1
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    Can't find derivative.

    Can somebody tell me how to find the rate of change to this?

    p = 240(1 - [3 / {3 + e^(-0.0005x)}]

    I need to find the rate of change when x = 1000.

    Thanks
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    Re: Can't find derivative.

    Quote Originally Posted by viper483 View Post
    Can somebody tell me how to find the rate of change to this?

    p = 240(1 - [3 / {3 + e^(-0.0005x)}]

    I need to find the rate of change when x = 1000.

    Thanks
    Just so we're clear, is this your function?

    \displaystyle \begin{align*} p = 240\left(1 - \frac{3}{3 + e^{-0.0005x}}\right) \end{align*}
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    Re: Can't find derivative.

    Quote Originally Posted by Prove It View Post
    Just so we're clear, is this your function?

    \displaystyle \begin{align*} p = 240\left(1 - \frac{3}{3 + e^{-0.0005x}}\right) \end{align*}
    Yes, that's correct. I need to learn how to set it out like that!
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    Re: Can't find derivative.

    Quote Originally Posted by viper483 View Post
    Yes, that's correct. I need to learn how to set it out like that!
    \displaystyle \begin{align*} p &= 240\left(1 - \frac{3}{3 + e^{-0.0005x}}\right) \\ &= 240 - \frac{720}{3 + e^{-0.0005x}} \\ &= 240 - 720\left(3 + e^{-0.0005x}\right)^{-1} \end{align*}

    You should be able to apply the Chain Rule now.
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    Re: Can't find derivative.

    Quote Originally Posted by Prove It View Post
    \displaystyle \begin{align*} p &= 240\left(1 - \frac{3}{3 + e^{-0.0005x}}\right) \\ &= 240 - \frac{720}{3 + e^{-0.0005x}} \\ &= 240 - 720\left(3 + e^{-0.0005x}\right)^{-1} \end{align*}

    You should be able to apply the Chain Rule now.
    Am I supposed to use the chain rule with the exponent of e as in f(p)=-0.0005x and use that as the inner function?

    My teacher said that when using the chain rule with an exponential function like this we're supposed to use the equation d/dx(e^f(x)) = e^f(x) * f '(x).

    I'm trying to use that for this equation but I don't think I'm supposed to because the answer doesn't make sense.
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    Re: Can't find derivative.

    There is no way for anyone to know where your answer makes sense or not if you don't tell us what answer you got!
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    Re: Can't find derivative.

    Quote Originally Posted by viper483 View Post
    Am I supposed to use the chain rule with the exponent of e as in f(p)=-0.0005x and use that as the inner function?

    My teacher said that when using the chain rule with an exponential function like this we're supposed to use the equation d/dx(e^f(x)) = e^f(x) * f '(x).

    I'm trying to use that for this equation but I don't think I'm supposed to because the answer doesn't make sense.
    I mean you let \displaystyle \begin{align*} u = 3 + e^{-0.0005x} \end{align*} which gives \displaystyle \begin{align*} y = 240 - 720u^{-1} \end{align*}

    You should be able to evaluate \displaystyle \begin{align*} \frac{du}{dx} \end{align*} and \displaystyle \begin{align*} \frac{dy}{du} \end{align*} then multiply them together...
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    Re: Can't find derivative.

    Quote Originally Posted by Prove It View Post
    I mean you let \displaystyle \begin{align*} u = 3 + e^{-0.0005x} \end{align*} which gives \displaystyle \begin{align*} y = 240 - 720u^{-1} \end{align*}

    You should be able to evaluate \displaystyle \begin{align*} \frac{du}{dx} \end{align*} and \displaystyle \begin{align*} \frac{dy}{du} \end{align*} then multiply them together...
    Sorry, it was midnight here last night, so ended up going to bed.

    Ok, so if it's \displaystyle \begin{align*} \frac{du}{dx} \end{align*} then

    u(1000)=3 + e^{-0.0005{1000}} which is 3.60653066...

    Using \displaystyle \begin{align*} \frac{dy}{du} \end{align*} it has to be

    y(u)=240 - 720 (3.60653066)^{-1}
    = 240 - 720 (0.277274781)
    =40.36

    Is this correct? The rate of change I should be getting is -0.0168?
    Last edited by viper483; August 6th 2012 at 06:31 PM.
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