# How do I take the derivative of my plot?

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Alejandro on 19 Apr 2013
Edited: Torsten on 23 Jan 2023 at 21:36
I have my temperature in the y axis, and my distance in the x. I have them all plotted out and I have the data too, how can I take the derivative of the plot?

Azzi Abdelmalek on 19 Apr 2013
dy=diff(y)./diff(x)
plot(x(2:end),dy)
Torsten on 23 Jan 2023 at 21:31
Edited: Torsten on 23 Jan 2023 at 21:36
If you only have discrete values for x and y, there is no method to tell you whether there is a discontinuity in the derivative of y in a point x_i.
You can compare (y(i+1)-y(i))/(x(i+1)-x(i)) with (y(i)-y(i-1))/(x(i)-x(i-1)), but even if both differ significantly, it's not possible to decide whether there is a discontinuity in the derivative at x=x(i).

Shaun VanWeelden on 19 Apr 2013
Call polyfit to generate your polynomial (if you don't already have a polynomial)
Call polyder to get derivative of your fitted line
Call polyval with your original X values to get the Y values of your derivative and plot that with hold on so it doesn't erase your original plot
John D'Errico on 31 Jul 2016
Note that polyfit (any polynomial fit) will often be a terribly poor choice here, since many curves are not well fit by a polynomial model. For example, consider points that lie on the perimeter of a circle, or the function sqrt(x), near x==0. Or the function sin(x), over multiple periods. Or a classic problem function for polynomial fits, 1/(1+x^2).