Listen here, Little Dicky

clearly, d/dx simplifies to 1/x

If not fraction, why fraction shaped?

I still don't know how I made it through those math curses at uni.

Why does using it as a fraction work just fine then?

This very nice Romanian lady that taught me complex plane calculus made sure to emphasize that e^j*theta was just a notation.

Then proceeded to just use it as if it was actually eulers number to the j arg. And I still don’t understand why and under what cases I can’t just assume it’s the actual thing.

Let's face it: Calculus notation is a mess. We have three different ways to notate a derivative, and they all suck.
I've seen e^{d/dx}

Division is an operator

Mathematicians will in one breath tell you they aren't fractions, then in the next tell you dz/dx = dz/dy * dy/dx

Have you seen a mathematician claim that? Because there's entire algebra they created just so it becomes a fraction.
(d/dx)(x) = 1 = dx/dx

What is Phil Swift going to do with that chicken?

The will repair it with flex seal of course
- To demonstrate the power of flex seal, I SAWED THIS CHICKEN IN HALF!

It was a fraction in Leibniz’s original notation.

And it denotes an operation that gives you that fraction in operational algebra...

Instead of making it clear that d is an operator, not a value, and thus the entire thing becomes an operator, physicists keep claiming that there's no fraction involved. I guess they like confusing people.

Derivatives started making more sense to me after I started learning their practical applications in physics class. d/dx was too abstract when learning it in precalc, but once physics introduced d/dt (change with respect to time t), it made derivative formulas feel more intuitive, like "velocity is the change in position with respect to time, which the derivative of position" and "acceleration is the change in velocity with respect to time, which is the derivative of velocity"

Possibly you just had to hear it more than once.

I learned it the other way around since my physics teacher was speedrunning the math sections to get to the fun physics stuff and I really got it after hearing it the second time in math class.

But yeah: it often helps to have practical examples and it doesn't get any more applicable to real life than d/dt.
- I always needed practical examples, which is why it was helpful to learn physics alongside calculus my senior year in high school. Knowing where the physics equations came from was easier than just blindly memorizing the formulas.
  
  The specific example of things clicking for me was understanding where the "1/2" came from in distance = 1/2 (acceleration)(time)^2 (the simpler case of initial velocity being 0).
  
  And then later on, complex numbers didn't make any sense to me until phase angles in AC circuits showed me a practical application, and vector calculus didn't make sense to me until I had to actually work out practical applications of Maxwell's equations.

I found math in physics to have this really fun duality of "these are rigorous rules that must be followed" and "if we make a set of edge case assumptions, we can fit the square peg in the round hole"

Also I will always treat the derivative operator as a fraction

I always chafed at that.

"Here are these rigid rules you must use and follow."

"How did we get these rules?"

"By ignoring others."
2+2 = 5

…for sufficiently large values of 2
- Found the engineer
- i was in a math class once where a physics major treated a particular variable as one because at csmic scale the value of the variable basically doesn't matter. the math professor both was and wasn't amused
- Engineer. 2+2=5+/-1
is this how Brian Greene was born?

Chicken thinking: "Someone please explain this guy how we solve the Schroëdinger equation"

Except you can kinda treat it as a fraction when dealing with differential equations

Oh god this comment just gave me ptsd
Only for separable equations

Look it is so simple, it just acts on an uncountably infinite dimensional vector space of differentiable functions.

fun fact: the vector space of differentiable functions (at least on compact domains) is actually of countable dimension.

still infinite though
- Doesn't BCT imply that infinite dimensional Banach spaces cannot have a countable basis

When a mathematician want to scare an physicist he only need to speak about ∞

When a physicist want to impress a mathematician he explains how he tames infinities with renormalization.

Is that Phill Swift from flex tape ?

Little dicky? Dick Feynman?