# Using undefined function in an expression

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

• Have a look at Dot. – b.gates.you.know.what Apr 20 '13 at 19:32
• he most certainly does not :P – Valentina Apr 20 '13 at 19:40

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