You made a LOT of mistakes.
delx = 1;
x = 0;
y = exp(x);
So you set x to zero. Then you evaluated exp(x).
That does NOT create a function of x. It simply evaluates exp(x), thus, here exp(0).
And I'm not sure what you think you are doing here:
yderivest = (y(2:end) - y(1:end-1))./delx;
y is a scalar variable. It is not a vector as you built it.
I'll give you a couple of suggestions to get you started.
Generate a vector of h values. Something like this:
h = 2.^(-20:1:0);
And you might create a function.
testfun = @(x) exp(x);
Now your code will work for other functions, doing not much more than changing testfun.
So what would this do?
x0 = 0;
fdiff = (testfun(x0 + h) - testfun(x0))./h
How would you change that for a central difference?
What is the error in the derivative approximation? Well, you know that the correct derivative is just:
truederiv = exp(x0);
fdifferr = abs(truederiv - fdiff);
Now you can plot the result as a function of h. Plot will work, but perhaps loglog will be a better choice of plotting tool. Think about why that might be true. What does the slope of such a resulting error plot mean when you plot it using loglog axes?
