How to take time derivatives of an function?

For example, f=cos(theta)+sin(beta)+theta_dot, and the first derivative of theta with respect to time t is theta_dot, and for beta is beta_dot. Then take derivatives of theta_dot and beta_dot again with respect to t are theta_dotdot and beta_dotdot respectively.

So take first derivative of f about t would be df/dt=-theta_dot*sin(theta)+beta_dot*cos(beta)+theta_dotdot. How can I write an function to achieve this?

Answer 1

[KSSV]

syms theta(t) beta(t)
f = cos(theta)+sin(beta)+diff(theta,t) ;
f_dot = diff(f,t)  % first derivative of wrt t
diff_dot2 = diff(f_dot,t)   % second derivative of wrt t

[Bokun Zhang]

Thanks you very much Siva for answering my question. I ran your code, and I'v got the expression of f_dot with diff() inside, which is f_dot(t) =

cos(beta(t))*diff(beta(t), t) - sin(theta(t))*diff(theta(t), t) + diff(theta(t), t, t)

Can I use theta_dot to take place the diff(theta,t) which is in the f_dot expression?

I try to solve this by writing another series of code but it gave me the same problem that the final expression is with the terms of diff().

Here is my code

syms t theta=sym('theta(t)'); gama=sym('gama(t)');

f=sin(theta)+cos(gama);

theta_dot=diff(theta,t); gama_dot=diff(theta,t);

df=diff(f,t)

the outcome is df =

cos(theta(t))*diff(theta(t), t) - sin(gama(t))*diff(gama(t), t)

[KSSV]

If you want to place theta_dot instead of diff(theta(t),t)...you can define it considering sym theta_dot(t)

[Bokun Zhang]

syms theta(t) beta(t) theta_dot(t) theta_dotdot(t) beta_dot(t) beta_dotdot(t)

theta_dot(t)=diff(theta(t),t); theta_dotdot(t)=diff(theta_dot(t),t); beta_dot(t)=diff(beta(t),t); beta_dotdot(t)=diff(beta_dot(t),t);

f=cos(theta)+sin(beta)+theta_dot; f_dot=diff(f,t)

I made some changes on the code but I still got this

cos(beta(t))*diff(beta(t), t) - sin(theta(t))*diff(theta(t), t) + diff(theta(t), t, t)

[KSSV]

Else you can use subs to substitute what you want..

Eg:

syms theta(t) beta(t)
f = cos(theta)+sin(beta)+diff(theta) ;
f_dot = diff(f,t) ; % first derivative of wrt t
f_dot = subs(f_dot,diff(theta(t), t, t),'theta_dot') ;
f_dot = subs(f_dot,diff(beta(t), t),'beta_dot') ;

[Bokun Zhang]

that helps much. thank you very much :)

[KSSV]

Thanking is accepting the answer.....:)

[mouad boumediene]

thnx

[abbas motallebi]

thanks

[Matthew Eddington]

THANK YOU!!!!!

Answer 2

[Lubah Nelson]

for i = 1:length(D)-2 f_D(i) = ( (-3*D(i)) + (4*D(i+1)) - (D(i+2))) / (2 * (D(i+1) - D(i))); end