Question about Symbolic Differentiation

Hello,

If I write the following code:

syms x t
answer = diff(x,t)

then answer = 0.

Is it possible to declare that x is some unknown function of t, so that diff(x,t) will return dxdt instead of 0?

(I'm asking because I'm trying to use MATLAB to automatically derive differential equations for certain user input for a specific application.)

Thank you,

Kevin

Answer 1

[Walter Roberson]

If you have a fairly new version of MATLAB (R2011b I think was the first), then

syms x(t)
diff(x,t)

[Azzi Abdelmalek]

don't work on (R2011b)

[Walter Roberson]

Ah yes, tracking back I find that R2012a was the first to support this.

[Kevin Bachovchin]

Thanks! It works on MATLAB 2012a, which I have.

However, is there still a way to maintain forcing x(t) to be a real number (instead of a complex number)?

Right now, I have

syms x1(t) x2(t) x3(t) real

It seems that when I added the function of t part, then MATLAB is treating x as a complex number instead of a real, which leads to "abs" and "conj" in my answer which I don't want.

[Walter Roberson]

assume(x1(t), 'real')

[Kevin Bachovchin]

Thanks again. When I try to take the partial derivative of function f with respect to x1(t), I'm getting an error saying Error using mupadmex Error in MuPAD command: Invalid variable. [stdlib::diff]

Is there any special way to take the partial derivative of f with respect to x1(t), or is it necessary to define a new syms x1 and substitute that in for x1(t) in f before taking the derivative?

[Walter Roberson]

It is not possible to take a derivative with respect to a function.