Comment on Listen here, Little Dicky
olafurp@lemmy.world 3 days ago
The thing is that it’s legit a fraction and d/dx actually explains what’s going on under the hood. People interact with it as an operator because it’s mostly looking up common derivatives and using the properties.
Take for example ∫f(x) dx
to mean "the sum (∫) of supersmall sections of x (dx) multiplied by the value of x at that point ( f(x) ). This is why there’s dx at the end of all integrals.
The same way you can say that the slope at x is tiny f(x) divided by tiny x or d*f(x) / dx
or more traditionally (d/dx) * f(x)
.
kogasa@programming.dev 3 days ago
The other thing is that it’s legit not a fraction.
jsomae@lemmy.ml 2 days ago
it’s legit a fraction, just the numerator and denominator aren’t numbers.
kogasa@programming.dev 2 days ago
No 👍
jsomae@lemmy.ml 2 days ago
try this on – Yes 👎
It’s a fraction of two infinitesimals. Infinitesimals aren’t numbers, however, they have their own algebra and can be manipulated algebraically. It so happens that a fraction of two infinitesimals behaves as a derivative.