Numerically derive a continous, non-symbolic function

I have a function defined via

function y = f(x)
    % ...
end

. I now want to numerically calculate the value of it's derivative at a given point. As in, what should be in the following function's body?

function y = derivative_of_f(x)
    % Calculate derivative of f at position x here
end

Is there any way to do this, without having to implement numerical differentiation myself?

Answer 1

[darova]

Derivative is (if you have numerical data)

dy = (y(i)-y(i-1)) / (t(i)-t(i-1));

Maybe diff (if you have a function) ?

syms x
diff(f(x))

[fi]

My function is not discretized yet, but continuous! This means I would first have to choose a precice enough discretization to use your method. That all is of course possible, but I was wondering whether there is an easier (built-in?) method where I don't have to reinvent the wheel. Kind of like the fzero function to find roots.

[darova]

Maybe diff?

syms x
diff(f(x))

[fi]

I don't think that will work here, since my function is not symbolic. For example, as soon as a function contains a case switch like this:

function y = f(x)
    if (x > 0)
        y = x^2;
    else
        y = x;
    end
end

...diff doesn't work anymore, throwing this error: Conversion to logical from sym is not possible.

Also, I don't want the analytical derivative, but just it's numerical approximation for a single given position.

[darova]

Another method

dx = 0.001;
dy = (f(x)-f(x+dx))/dx;

[fi]

Yeah, that's seems like the easisest way.

I just wanted to know if there is a preferred, maybe built-in way where I don't have to take care of precision. Anyway, thanks alot!

[darova]

Can you accept the answer please

[fi]

Well, the answer is currently in your comment and there is no accept button for that :(

Could you maybe edit you original answer?

[darova]

yes please