Most beginning calculus students would like differentiation to behave
better.  It would be nice, for example, if the product rule and the
quotient rule were simpler.

Are there two functions f and g that have the property that the derivative
of their product fg is the product of their derivatives and the derivative
of their quotient f/g is the quotient of their derivatives?  We require
the functions to have derivatives at every point, and of course neither g
nor g' can be zero, since f/g and f'/g' are supposed to make sense.

(This problem appeared as Macalester College math problem of the week
#738.)

There will be a $1 prize for the best correct solution submitted by a
midshipman.

A solution is "correct" if it answers the question correctly and explains
the answer; a solution is "best" if it includes the clearest correct
explanation.  Solutions are due by noon on Wednesday, January 27, 1999.
Submit solutions to Prof. Hanna at mathprob@nadn.navy.mil, or via the
mailbox in Chauvenet 301.


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Correct solutions to problem #83, the cube inside the cone, came from
Midn. 1/c Rex, Midn 3/c Estes, Lusk, and Rivera, Midn 4/c Chen, CDR
Cameron, and J. Meuller, who describes himself as "Midn. Hopeful 04."  The
prize goes to Mr. Rivera, whose solution is posted on the bulletin board
in the Chauvenet lab deck corridor (along with CDR Cameron's, which had
the best picture).