At every value of x, how measure slope of plot?

clear all

clc

x=[15 20 25 30 35 40 45 50 55];

y=[11.89 11.845 11.85 11.855 11.865 11.93 12.01 12.2 12.77];

plot(x,y)

Answer 1

[Torsten]

Look at the approximate slope curve under

https://de.mathworks.com/matlabcentral/answers/1919960-how-can-i-interpolate-x-and-y-data-points-in-plot-and-slope-dy-dx-at-any-value-of-x?s_tid=srchtitle

You cannot expect a simple explicit equation for it.

A possible function is given here as dy:

X=[15 20 25 30 35 40 45 50 55];
Y=[11.89 11.845 11.85 11.855 11.865 11.93 12.01 12.2 12.77];
dY = gradient(Y,5);
dy = @(x) interp1(X,dY,x)

dy = function_handle with value:
    @(x)interp1(X,dY,x)

dy(22.8)

ans = -0.0012