Decoding Leibniz Notation (2024)

Math nerds brawl over df/dx—rules vs vibes

TLDR: The article explains that df/dx is a formal symbol for change, not a fraction you can cancel. Comments exploded into purists vs pragmatists: some demand strict rules, others brag they “do algebra” with it because it works, arguing over how calculus should actually be taught.

A calm explainer on Leibniz notation—aka the famous “df/dx” symbol for change—hit the timeline and instantly sparked a nerdy street fight. The post says df/dx isn’t a real fraction you can cancel; it’s a symbol that stands for the derivative, with history’s “tiny changes” idea only a helpful story. Cue the split: purists cheered the “no, you can’t cancel the d’s” mantra, while the pragmatists rolled up with “we do it anyway because it works.”

Top commenter tptacek poked the bear: people literally do algebra with df/dx during substitution in calculus class, and everyone’s guilty. Another voice, sixo, linked Putting Differentials Back into Calculus, basically saying: stop pretending; teach the moves that actually get results. The drama peaked around the second derivative’s messy d²f/dx² notation—should it be (dx)²? Is any of this “real” algebra? The thread turned into a meme factory: “Cancel the d’s? Only if you want your grade canceled,” “df/dx is vibes-first math,” and “engineers don’t care, it gets the job done.”

Verdict from the crowd: the post is a clean tour through the chaos, but the community can’t resist the eternal fight—strict rules vs useful hacks—and df/dx is the hill they’ll die on.

Key Points

  • Leibniz notation historically treated derivatives as ratios of infinitesimal changes df and dx.
  • In modern mathematics, df/dx is a single symbol denoting the derivative function f′, not a literal quotient.
  • The derivative in Leibniz notation denotes a function; evaluation at a point corresponds to f′(a).
  • Second derivatives are written d²f/dx²=f′′ by symbolic convenience, not by true algebraic squaring.
  • Algebra-like manipulations in Leibniz notation (e.g., dx² vs. (dx)², d²) are conventional shortcuts, not formal algebra.

Hottest takes

"There's other goofy stuff people do with df/dx" — tptacek
"In a u-substitution you literally do 'algebra' with it" — tptacek
"Related: 'Putting Differentials Back into Calculus'" — sixo
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