How can I interpolate x and y data points in plot and slope (dy/dx) at any value of x?

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]

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];
% Approximate dy/dx
dy = gradient(y,5);
hold on
yyaxis left
plot(x,y)
ylabel('y vs. x') 
yyaxis right
plot(x,dy)
ylabel('dy/dx  vs. x')
hold off
grid on

% interpolate y and dy/dx at x=x0
x0 = 22;
y0 = interp1(x,y,x0)

y0 = 11.8470

dy0 = interp1(x,dy,x0)

dy0 = -0.0020

[MOHD UWAIS]

Can we have slope equation like dy/dx in terms of x?

[Torsten]

But you also didn't give us an equation for y in terms of x ... So isn't it natural that you also only get dy/dx as a vector of 9 values from the command dy = gradient(y,5) and that you have to interpolate between the values to get y and dy/dx for some given value of x in between 15 and 55 ?

[MOHD UWAIS]

Thank you for your response