There are several ways to compute the derivative numerically, cf.
help diff
but this can be noisy, and isn't terribly precise for data with large gaps. If this is truly data, you might want to look at the loglog plot
loglog(x, y, '.')
You'll see it's very nearly linear in log-log.
Assuming you're not using any toolboxes, you can look at
help ployfit
to perform a regression on log(x), log(y), or use the backslash operator to find a linear fit.
x=[0.01324, 0.152784,1.426024,14.76958,147.6958,1527.888,15229.85];
y=[0.0000025,0.0000075,0.000025,0.000075,0.00025,0.0008,.0025];
n = numel(x);
X = log(x(:));
Y = log(y(:));
M = [ones(n, 1), X]\Y;
C = exp(M(1));
b = M(2);
loglog(x, y, '.', x, C*x.^b);
Now that you have a good fit for your data, use the expression C*x.^b to interpolate it, and analytically compute your derivative for any value of x.
This isn't exactly what you asked, so let me know if this helps (or if you truly prefer a numerical derivative, and are struggling with diff).
--Andy
