This variable is undefined for derivative

[SS_9781956]

I am unable to get the evaluation of Derivative in attached worksheet.  How do I get it evaluated? 

[terryhendicott]

Hi,

Need to define a value for Rho typically density so I chose air at 1.25kg/m^3.

Cheers

Terry

[Werner_E]

Your sheet does not work - maybe due to an error in the protected area. First error message is that rho is not defined.

But the problem is clear anyway: A solve block with odesolve returns a numerical solution, not a symbolic one. You don't get a symbolic function definition and so you can't demand a symbolic derivative.

All you can do is to numerically evaluate the functions at positions within the interval from 0 to 20 s and you may also numerically evaluate their derivatives as you already did in the plot. So Phi(2s)= will work, but Phi(t)= or Phi(t)-> can't - apart from the fact that you already defined t as a range!

Starting with version 9 PTC implemented a way to symbolically solve some simple ODEs and systems of ODEs See Solving ODEs Symbolically

If you are in need for a symbolic solution you may give that a try.

EDIT: In case that your intention was to just make some sort of table of values, you should not use a range but rather a vector of t-values and call the function vectorized.

The derivatives may fail at the end postions (0s and 20s) because the numeric algorithm needs neigbour-points which do not exist at the ends of the interval. Nonetheless you may filter the failing values and still see the other values or you define a vector of t-values which does not include the problematic end values.
For more help and showing what I mean we would need a working sheet of course.

[Werner_E · Accepted solution]

As Terry kindly provided a working sheet by adding an appropriate value for rho, here some additional remarks:

The calculation of the derivatives fails because of the end values (0s, 20s) as already explained

You may fix this by using try & catch

It may be worth to define a small utility function to do that job

!! !BUT ,,,

You can't assign these values to a variable for later use as its NOT a vector! So of course vectorization does not help at all

Despite of the misleading error message the true reason is (as written in my previous answer) that t is a range, not a vector!.

There is an undocumented trick to turn a range into a vector by following the assignment with an inline evaluation:

t_vec is now a legitimate vector, not a range (unfortunately ranges and vectors look the very same in Prime).

A more "legal" way to create that very same vector is seen here:

Now you can use this vector to create a table for later use - don't forget about vectorization (the arrow over the expression)

or create a more comprehensive table

But of course you still can't evaluate the functions and their derivatives symbolically as you tried to do because the functions derived by OdeSolve are numeric only.