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Math Bite: Once in a While, Differentiation is Multiplicative Many students of calculus would be a lot happier if the Leibniz formulas
 

Summary: Math Bite: Once in a While, Differentiation is Multiplicative
Many students of calculus would be a lot happier if the Leibniz formulas
(fg) = f g + fg and
f
g
=
f g - fg
g2
,
where f denotes the derivative of f, could be replaced by the much simpler formulas
(fg) = f g (1)
and
f
g
=
f
g
. (2)
Discovering exactly when the usually erroneous equations (1) and (2) are valid is a
simple but neat exercise involving three separable differential equations. Paul Zorn

  

Source: Ash, J. Marshall - Department of Mathematical Sciences, DePaul University

 

Collections: Mathematics