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Subject: "Derivative Needed!"     Previous Topic | Next Topic
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Conferences The CTK Exchange High school Topic #171
Reading Topic #171
May-19-02, 07:48 AM (EST)
"Derivative Needed!"
   Hi, I need help to find the derivative of this equation:

y = (1000*0.96^t)* e^3.247 * e^(0.0873*80(1-0.96^t))
Any help muchly appreciated. Thanks

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Member since Nov-16-01
May-20-02, 08:38 AM (EST)
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1. "RE: Derivative Needed!"
In response to message #0
   I think your notation is getting in your way - if you clean it up the problem will become a lot easier.
I will start by replacing the numbers with constants. What you have written (if I understand it right) can be represented by

y = k.at.e(bt) for some a,b,k (using . for multiplication)

note that d/dt(at) = d/dt(et.ln(a)) = ln(a).et.ln(a) = at.ln(a)
and therefore by the chain rule
d/dt(e(bt)) = bt.e(bt).ln(b)

so using the product rule:

d/dt(y) = k.{ at.ln(a).e(bt) + at.bt.ln(b).e(bt) }

now you need to evaluate a,b,k from your original expression and plug them in.

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