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Not able to apply derviatives to a simple situation

  1. Oct 31, 2012 #1

    I am confused by this relatively simple problem.

    The operating margin of a business = (Revenue – costs)/Revenue
    M = (R-C)/R = 1 – C/R

    Now I wish to find the sensitivity of M to changes in R. So I try to differentiate the equation by R

    dM/dR = C/R^2

    But this equation doesn’t make any sense to me. For example, consider this figures: R=100, C=38,
    If R increases by 1%, M increases by 0.38%.

    I am not sure what I am doing wrong.

  2. jcsd
  3. Oct 31, 2012 #2


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    Science Advisor

    The derivative is not a percentage, it is a ratio:
    If R= 100, C= 38 then M= 1- 38/100= .62. If R= 101, C= 38 then M=1- 38/101=.6238 so M has increased by .0038 which, divided by R, not M, is .38
  4. Oct 31, 2012 #3
    Thanks HallsofIvy, but I am still confused.

    When R increases by 1%, M increases by 0.38%. Thus the rate of change is 0.38.
    But this answer still doesn't match with the derivative (dM/dR = C/R^2).
  5. Oct 31, 2012 #4
    I also have a sub question.

    How would you differentiate the following equation with R, where C is a constant. I am interested in the notation. Is my notation correct?

    N = R - C

    dN/dR = R * dR/dR
  6. Oct 31, 2012 #5


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    Science Advisor

    No, it isn't. Again, the derivative of the constant, C, is 0 so dN/dR= dR/dR= 1.
  7. Oct 31, 2012 #6

    Do you think the following derivative is correct?

    M = (R-C)/R = 1 – C/R

    dM/dR = C/R^2
  8. Oct 31, 2012 #7


    Staff: Mentor

    Yes, it's correct.
  9. Oct 31, 2012 #8
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