How to calculate the derivative of any function f(x) at x=0 using finite difference method?

Let's say I have any unknown function and I know its value for some x i.e.

for

x=1:10

is

f(x)=[a b c d e f g h i j k l m]

where are some numerical values.

Can I calculate derivative of at with this given data?

Answer 1

[Star Strider]

if ‘a,b,c’ are numerical values and not functrions of ‘x’, the derivative would be uniformly 0.

[Luqman Saleem]

actually values in matrix f(x) depend upon x. Derivative can be calculated using any numerical method. Is it not like this?

Let me put it in this way, let f(x)=sin(x)

now x=1:10 and

f(x)=[0.8415 0.9093 0.1411 -0.7568 -0.9589 -0.2794 0.6570 0.9894 0.4121 -0.5440]

Can't we find derivative of f(x) now with respect to x?

[Star Strider]

To calculate a numerical derivative, use the gradient function:

f = @(x) sin(x);
x = 1:10;
y = f(x)
dydx = gradient(y, mean(diff(x)))

figure
plot(x, y,    x, dydx)
grid

Here, ‘x’ is regularly spaced.

For irregularly-spaced ‘x’, an acceptable alternative is:

dydx = gradient(y)./gradient(x).  

[Luqman Saleem]

Thank you.

[Star Strider]

As always, my pleasure.