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?

10 views (last 30 days)
I apologize for such a poorly worded question, but I'm not quite sure how else to word it.
You're given, x and y, both symbolic variables as a function of time. y is also a function of x. You determine the time derivative of y, ydot. xdot also appears in ydot because y is a function of x, and x is a function of time. How do you then differentiate ydot with respect to xdot?
Here's my code:
syms y x(t) t
y = sin(x);
ydot = diff(y,t);
I've also tried this method:
syms y x(t) t
y = sin(x);
ydot = diff(y,t);
syms Dx
ydot = subs(ydot,sym('D(x)'),Dx);
But that gives me an output of:
ans(t) = 0
The answer should be cos(x(t))

Accepted Answer

Walter Roberson
Walter Roberson on 9 Aug 2013
No. MuPAD can only differentiate with respect to a variable, not with respect to a function.
  1 Comment
Dominic on 5 Mar 2023
You have to create the general diff function for partial differentiation. You can perform this using the limit definition of the derivative with an h value as close to 0 as possible. You can program in the algebraic steps to simplification and then return the resultant expression. This will work for any type of function assuming the derivative is well defined.

Sign in to comment.

More Answers (1)

Paul on 5 Mar 2023
syms y x(t) t
y = sin(x);
ydot = diff(y,t)
ydot(t) = 
syms Dx(t)
ydot(t) = subs(ydot,diff(x,t),Dx(t))
ydot(t) = 
ans(t) = 

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!