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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- Aug 6th 2012, 04:19 AMviper483Can'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 - Aug 6th 2012, 04:40 AMProve ItRe: Can't find derivative.
- Aug 6th 2012, 04:41 AMviper483Re: Can't find derivative.
- Aug 6th 2012, 04:53 AMProve ItRe: Can't find derivative.
- Aug 6th 2012, 05:18 AMviper483Re: Can't find derivative.
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. - Aug 6th 2012, 05:34 AMHallsofIvyRe: 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!

- Aug 6th 2012, 05:58 AMProve ItRe: Can't find derivative.
I mean you let $\displaystyle \displaystyle \begin{align*} u = 3 + e^{-0.0005x} \end{align*}$ which gives $\displaystyle \displaystyle \begin{align*} y = 240 - 720u^{-1} \end{align*}$

You should be able to evaluate $\displaystyle \displaystyle \begin{align*} \frac{du}{dx} \end{align*}$ and $\displaystyle \displaystyle \begin{align*} \frac{dy}{du} \end{align*}$ then multiply them together... - Aug 6th 2012, 03:26 PMviper483Re: Can't find derivative.
Sorry, it was midnight here last night, so ended up going to bed.

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

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

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

$\displaystyle y(u)=240 - 720 (3.60653066)^{-1}$

$\displaystyle = 240 - 720 (0.277274781)$

$\displaystyle =40.36$

Is this correct? The rate of change I should be getting is -0.0168?