Learn how to a build a cloud-first strategyRegister Now

x
?
Solved

Derivation of a Derivative

Posted on 2008-11-07
3
Medium Priority
?
450 Views
Last Modified: 2012-05-05
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
0
Comment
Question by:sublimation
  • 2
3 Comments
 
LVL 53

Accepted Solution

by:
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
0
 
LVL 4

Author Closing Comment

by:sublimation
ID: 31514283
That is plush!
0
 
LVL 53

Expert Comment

by:Infinity08
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)
0

Featured Post

Important Lessons on Recovering from Petya

In their most recent webinar, Skyport Systems explores ways to isolate and protect critical databases to keep the core of your company safe from harm.

Question has a verified solution.

If you are experiencing a similar issue, please ask a related question

Have you ever thought of installing a power system that generates solar electricity to power your house? Some may say yes, while others may tell me no. But have you noticed that people around you are now considering installing such systems in their …
When we purchase storage, we typically are advertised storage of 500GB, 1TB, 2TB and so on. However, when you actually install it into your computer, your 500GB HDD will actually show up as 465GB. Why? It has to do with the way people and computers…
This is a video describing the growing solar energy use in Utah. This is a topic that greatly interests me and so I decided to produce a video about it.
I've attached the XLSM Excel spreadsheet I used in the video and also text files containing the macros used below. https://filedb.experts-exchange.com/incoming/2017/03_w12/1151775/Permutations.txt https://filedb.experts-exchange.com/incoming/201…
Suggested Courses

810 members asked questions and received personalized solutions in the past 7 days.

Join the community of 500,000 technology professionals and ask your questions.

Join & Ask a Question