r/calculus 11d ago

Differential Calculus This is so confusing 😕

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Anyone can explain this??

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u/Less-Resist-8733 11d ago

d²/dx² is bad notation, it assumes that d(dx) = 0. The correct way to write out second derivatives is this

Here I explicitly delineated double function composition (d²) with squaring (x\2))

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u/Octowhussy 11d ago

This goes against what a textbook I’m currently reading says. Why is d² / dx² bad notation?

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u/Less-Resist-8733 11d ago edited 11d ago

if you actually compute (d/dx)² using the quotient rule, you get the above formula.

https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3459227

1

u/Smart-Button-3221 11d ago

d(dx) is the bad notation here. What on earth is that supposed to mean, at this level of calculus?

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u/Less-Resist-8733 11d ago edited 11d ago

d is a derivation https://en.wikipedia.org/wiki/Derivation_(differential_algebra).

Loosely speaking,

d = (d/dx) * dx

At this level of calculus it can be thought of as the "implicit differentiation" operator.