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# Derivation of a Derivative

Posted on 2008-11-07
Medium Priority
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Hi, mathe experts...

I am looking at a calculus intoduction and I am not sure how something was derived, I am pretty good at re-arranging normal formulas but a bit stuck here.

How do we get from:

P = C/(1+r) + C/(1+r)^2 + C/(1+r)^3 + ... + C/(1+r)^9 + C/(1+r)^9 + par/(1+r)^10

to:

dP/dr = -C/(1+r)^2 + -2C/(1+r)^3 + ... -10C/(1+r)^11 + -10 par/(1+r)^11

I know thas the diff of x^2 = 2x
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Question by:sublimation
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Accepted Solution

Infinity08 earned 2000 total points
ID: 22902947
Since P is a sum, you can differentiate every term separately. They are all of the form :

C / (1 + r)^n

This is the same as :

C * (1 + r)^(-n)

The derivative of that is :

C * (-n) * (1 + r)^(-n - 1) * d(1+r)/dr = -C * n / (1 + r)^(n + 1)

So, for the second term (n = 2) :

C/(1+r)^2

we get the derivative :

-2C / (1 + r)^3
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Author Closing Comment

ID: 31514283
That is plush!
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LVL 53

Expert Comment

ID: 22903001
btw :

>> I know thas the diff of x^2 = 2x

This applies the exact same rule :

d (x^n) / dx = n * x^(n - 1)
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