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I want to use undefined functions in expressions to be simplified. For example.

I want mathematica to simplify this input

$(f^{\prime\prime}(t),g^{\prime\prime}(t))\cdot (-g^\prime(t),f^\prime(t)) $

into this output:

$f'(t)g''(t)- f''(t)g'(t)$.

How does one go about the "Simplify" command for that first expression in order to get the second one? How do you specify that $f$ is a function of $t$, without of course defining it, in an expression?

Cheers

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    $\begingroup$ Have a look at Dot. $\endgroup$
    – b.gates.you.know.what
    Apr 20 '13 at 19:32
  • $\begingroup$ he most certainly does not :P $\endgroup$
    – Valentina
    Apr 20 '13 at 19:40
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You can define the derivative of a function easily: D[f[t], {t, 1}] is the first derivative of the (unspecified) function f[t]. So your expression is:

{D[f[t], {t, 2}], D[g[t], {t, 2}]}.{-D[g[t], {t, 1}], D[f[t], {t, 1}]}

which nicely returns the desired expression.

You will likely benefit from exploring the documentation a little. For instance, had you looked into the docs for the derivative function by typing

?Derivative

or the simpler form

?D

you would have been able to answer your own question.

`

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  • $\begingroup$ Thanks for the great answer! My issue with the documentation was in understanding that I could input f[t] without having to define f[t] somewhere earlier in the code. $\endgroup$
    – dolphus333
    Mar 2 '15 at 20:34

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