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Question
Hi Randy,

I don't know how to take the derivative of the 2 below function.

g(N)=rN(a-N)(1-N/k)
differentiate in respect of N; a,k and r are just constants.

f(N)=r(aN-N^2)(1-N/k)
differentiate in respect of N; r, k and a are just constants.

I tried to simplify them and them both seem to simplify into the same function.

Many Thanks for all your help,
Sam.

Answer
The easiest way to take the derivatives is to first multiply out the terms and then use the easy formula for derivatives:

d(cx^m)/dx = mcx^(m-1)   where c is a constant (or at least not a function of x).

So I get

g(N) = rN(a-N)(1-N/k) = raN-rN^2-raN^2/k+rN^3/k  and

dG(N)/dN = ra-2rN-2raN/k+3rN^2/k.

The other function is the same if you multiply it out.

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randy patton

Expertise

college mathematics, applied math, advanced calculus, complex analysis, linear and abstract algebra, probability theory, signal processing, undergraduate physics, physical oceanography

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26 years as a professional scientist conducting academic quality research on mostly classified projects involving math/physics modeling and simulation, data analysis and signal processing, instrument development; often ocean related

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J. Physical Oceanography, 1984 "A Numerical Model for Low-Frequency Equatorial Dynamics", with M. Cane

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M.S. MIT Physical Oceanography, B.S. UC Berkeley Applied Math

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Also an Expert in Oceanography

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