# Not able to apply derviatives to a simple situation

1. Oct 31, 2012

### musicgold

Hi,

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.

Thanks.

2. Oct 31, 2012

### HallsofIvy

Staff Emeritus
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

3. Oct 31, 2012

### musicgold

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).

4. Oct 31, 2012

### musicgold

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

5. Oct 31, 2012

### HallsofIvy

Staff Emeritus
No, it isn't. Again, the derivative of the constant, C, is 0 so dN/dR= dR/dR= 1.

6. Oct 31, 2012

### musicgold

Thanks.

Do you think the following derivative is correct?

M = (R-C)/R = 1 – C/R

dM/dR = C/R^2

7. Oct 31, 2012

### Staff: Mentor

Yes, it's correct.

8. Oct 31, 2012

Thanks.