Analyze g Differentiate

Calculates the derivative of the selected plots. This can be done in two ways. 

g Direct
Calculates the DY/DX between two data points, and places the result in the middle of them. This means that your resulting plot will have one data point less than the original plot. It can be handy if you need to have the derivative of every single line between data points in your graph, but the results can be pretty noisy, and even erroneous if the X values aren't equidistant. 

In most cases the smoothed calculation with a width of 1 is more accurate than the direct calculation. The smoothed calculation also leaves your number of data points and their X values alone. The direct calculation should only be used to determine the exact location of a sudden jump in direction, or if you really need the DY/DX of every single line between the data points in your graph.

g Smoothed
Takes the derivative of the two points surrounding a data point, and places the result over the data point in the middle. This makes the result a lot less noisy, and is the preferred method to use. 

You will be asked for the width factor. A width of 1 is the most accurate, as it takes the DY/DX of the data points directly adjacent to the source data point, which is the same as taking the DY/DX of both lines originating from the source data point, and averaging the outcome. By increasing the width you will increase the "number of data points away from the source point" from which the derivative will be taken. The larger the width, the smoother the result will be, but very high factors can give erroneous results, and the phase will be smeared out as well. 

The effect of using different widths

You have to experiment a bit to get the optimum between smoothness and accuracy. To check if a derivative is correct, integrate it after taking the derivative, you should get your original plot back, apart from the starting offset which is lost by differentiating.