  In 1857 Sylvester stated a result on determinants without proof that was
recognized as important over the subsequent century. Thus it was a surprise to
Akritas, Akritas and Malaschonok when they found only one English proof - given
by Bareiss 111 years later! To rectify the gap in the literature these authors
collected and translated six additional proofs: four from German and two from
Russian. These proofs range from long and "readily understood by high school
students" to elegant but high level.
  We add our own proof to this collection which exploits the product rule and
the fact that taking a derivative of a determinant with respect to one of its
elements yields its cofactor. A differential operator can then be used to
replace one row with another.
