Derivative without diff function

Hi everyone,

So I have this problem, my university is giving us an assignment where we have to find the derivative without using the diff function. So we have an array of positions(y) and an array of time(t) and we have to find the derivative in order to find the speed.

I know I have to use this function (f(x + h) - f(x - h)) / (2*h), so I came up with this code:

fun = @(y,t) y/t;

dx = t(2)-t(1);

x = y(1);

df = (fun(x + dx) - fun(x - dx)) / (2*dx);

But it is giving me errors, specifically "Not enough input arguments. Error in @(x,t)x/t". What is the error? How can I calculate the derivative in order to find the speed?

Thanks in advance.

[Walter Roberson]

I suggest you use gradient()

Answer 1

[KSSV]

You should proceed something like this:

fun = @(y,t) y/t;

t = linspace(0,60,500) ;
y = sin(t) ;

df = zeros(length(t)-1) ;

for i = 1:length(t)-1
    dx = t(i+1)-t(i);
    x = y(i);
    df(i) = (fun(x + dx,t(i)) - fun(x - dx,t(i))) / (2*dx);
end

[SAYGIN ileri]

Would you mind writing an example for derivation for chain rule, please..

Answer 2

[Jan]

"Not enough input arguments. Error in @(x,t)x/t"

You have defined fun to use 2 input arguments:

fun = @(y,t) y/t;

But in fun(x + dx) you provide 1 input only.

"So we have an array of positions(y) and an array of time(t)"

This means, that you cannot determine f(x+h), because all you have is the numerical values of y and t. Then:

dy = (y(3:end) - y(1:end - 2)) ./ (t(3:end) - t(1:end-2))