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Analysis of a derivative

  1. Aug 4, 2010 #1
    Hi

    I am not sure if my interpretation of the following derivative is correct.

    N = I / R - D

    Where , N, I and D are integers, while R is a fraction (1% to 15%).

    If I differentiate the above equation with respect to R, I get the following equation.

    dN/dR = I / R^2

    The following is my interpretation of this derivative.

    1. The lower the value of R, the higher the value of dN/dR, at a given I

    2. At a given R, the higher the value of I , the higher the value of dN/dR

    3. If I plot dN/dR against R, at various values of I, I will get exponentially declining curves, with curves with higher I values lying on the left of curves with lower I values.



    Thank you,

    MG.
     
  2. jcsd
  3. Aug 4, 2010 #2

    Mark44

    Staff: Mentor

    You should have dN/dR = -I/R2. Also, when you differentiate a variable, you are assuming tacitly that it can take on all real values in some interval. You can evaluate the derivative at integer values.
    1. The smaller R is the more negative dN/dR will be (assuming that I > 0).
    2. For a given R, the larger I is, the more negative dN/dR will be (again assuming that I > 0).
    3. Take into account that you had the wrong sign for your derivative.
     
  4. Aug 5, 2010 #3

    Mute

    User Avatar
    Homework Helper

    The highlighted part is incorrect. Exponential curves are of the form [itex]b^{\pm a x}[/itex], where x is the variable and so would be your R. The plus sign corresponds to exponential growth as x gets large and the minus corresponds to exponential decay as x gets large.

    The behaviour of the derivative you give is that it varies inversely as a quadratic. (Inversely means 1/x and quadratic means x^2).
     
  5. Aug 8, 2010 #4
    thanks folks.
     
  6. Aug 9, 2010 #5
    I believe your derivative should be ........

    dN/dR = - I / [ R - D ]^(- 2)

    That just causes a shift of the graph D units to the right.
     
  7. Aug 9, 2010 #6

    Mark44

    Staff: Mentor

    You are interpreting the original equation, N = I/R - D as if it had been written N = I/(R - D). I am working with the equation exactly as it was written, which is the same is if it had been written N = (I/R) - D.
     
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