I can never remember the quotient rule for derivatives. You know, (x/y)' = ?. So I got out the computer algebra package Maxima and had this little session:
(%i56) ratsimp(diff(x(t)/y(t),t));
d d
x(t) (-- (y(t))) - y(t) (-- (x(t)))
dt dt
(%o56) - -----------------------------------
2
y (t)
Spot the minus sign next to the horizontal rule, separated by a single space? I didn't. Think it is insane not to absorb that minus sign into the numerator by swapping the terms? I do.
There's a half-hour of my life I'll never get back… Update: I finally got access to Maple and tried it there. Much better:
> simplify(diff(x(t)/y(t), t));
/d \ /d \
|-- x(t)| y(t) - x(t) |-- y(t)|
\dt / \dt /
-------------------------------
2
y(t)
However, a look at the unsimplified form reveals that there are still "issues":
> diff(x(t)/y(t), t);
d /d \
-- x(t) x(t) |-- y(t)|
dt \dt /
------- - --------------
y(t) 2
y(t)
Recommendation for CA implementers; two spaces between a minus sign and a horizontal bar, please. (B)