# First Derivative

1. Aug 16, 2013

### rovaniemi

Hi,

The data in the excel sheet is the numerical representation of the image of leafs taken through spectral imaging camera. The first column represents the wavelength range and other three are the chlorophyll measurements of leaves form 3 different locations. I would like to find out is, if there is any difference in chlorophyll level in these 3 different places. Could anyone please tell me how can i find the first derivative for the given data?

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• ###### Book1.xlsx
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2. Aug 16, 2013

### Staff: Mentor

First derivative of what?

I plotted the values and then the deviations from the average for each wavelength. I think the result is interesting:

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3. Aug 17, 2013

### rovaniemi

Hi,

Thanks for the reply. Could you please tell me, how did you calculate the first derivative? I would like to find the first derivative of columns North, North East and South. Can the first derivative be obtained by subtracting two consecutive function values, then dividing them by the difference in the independent variables (Wavelengths in this case)?

I have also found a formula to find the first derivative. I don't know if it can be used in this situation.
The formula is "x^n for first derivative and n x^n-1 for second derivative.

Good day

Last edited: Aug 17, 2013
4. Aug 17, 2013

### Staff: Mentor

I did not calculate any derivatives, and I don't think there are any meaningful derivatives.
They can be approximated like that, but I don't see what you would learn from the resulting values.
That is not a formula.

5. Aug 17, 2013

### rovaniemi

Hi,

I am not good at calculus. I just need to find the rate of change in the chlorophyll content at different regions. The attachment shows the approximated first derivative graph and if i am not wrong that doesn't show any significant change.

Formula or rule what you say in calculus; i got those by goggling. But i am not able to understand its application in biology. Anyway i tried the approximated derivate.

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6. Aug 17, 2013

### Staff: Mentor

I think you are mixing completely unrelated things here.

You have three samples. Each sample has some specific chlorophyll content, right? So you just have 3 (not yet known unknown) values for chlorophyll contents.

Each chemical composition (including the chlorophyll content) leads to a specific spectrum. You can analyze this spectrum to get the chlorophyll content of a sample, for one sample at a time. This will need some external data - how does the spectrum of chlorophyll look like?
Once you know this (and, ideally, the spectra of other chemicals in your sample), you can look for this signature in your samples, and find some (relative) value for the chlorophyll content in your samples.

It is pointless to calculate derivatives in the spectrum - each data point has a completely different meaning (the absorption or emission at a specific wavelength range).