MATLAB: How to take time derivatives of a function

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My objective is to take the first and second time derivatives of my function for displacement 'x'. I have it modelling a function of displacement over angle with respect to time. Does MATLAB have a function that represents dx/dt? Here are the analytical solutions and my code for reference.

h = 60 ; 
b =130 ; 
r = 28 ; 
w = 2*pi; % angular velocity
t =0:(1/36):1 ; 
x = b*(r*sin(w*t))./(h-r*cos(w*t));

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dxdt = diff(x)./diff(t) ;   % derivative of x w.r.t t

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MATLAB: Second time derivative of function

It does not work, because the length of diff(x) and diff(t) are not the same. diff function takes the difference between each element. However returns 1 element less than the original vector since there is no way to find the difference for the last element.

Since you have fixed step size you can use

v = diff(x)./(1/36); 
td = t(1:end-1); % time vector for plotting first derivative
a = diff(v)./(1/36) ;tdd = t(1:end-2)    
tdd = t(1:end-2); % time vector for plotting second derivative

Alternatively you might try symbolic toolbox to derive the derivative of the expression symbolicly and then plug in numbers.

MATLAB: After taking the time derivative of a symbolic expression, how do you then differentiate that new expression with respect to another variable’s time derivative

No. MuPAD can only differentiate with respect to a variable, not with respect to a function.

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MATLAB: Second time derivative of function

MATLAB: After taking the time derivative of a symbolic expression, how do you then differentiate that new expression with respect to another variable’s time derivative

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