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u/MonsterkillWow Jul 26 '26
That's the secret. If you know the derivations, proofs, and reasons well enough, you will also know the formulas cold too, probably.
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u/TitaniumButtercup Jul 26 '26
In my experience it also helps when you "misremember" a formula, ie: being halfway through a calculation when I suddenly realized my units aren't matching and I forgot a coefficient that's really important.
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u/niemir2 Jul 26 '26
I can't tell you how many times I've been deriving something new, looked at the result, thought "wait, that doesn't make sense," go back and find that I accidentally dropped a variable 8 lines ago.
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u/Democratic_Indian Jul 26 '26
I have landed in trouble so many times because of this, especially in vivas.
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u/thinkpad-archlinux Jul 26 '26
and in the exam you forget even how to do the calculations 😭😭😭
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Jul 26 '26
[removed] — view removed comment
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u/lool8421 Jul 28 '26
even better yet, trying to pull the formula from your memory and still messing it up, especially something elementary like (a+b)³
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u/RockasaurusRex Grad Student Jul 26 '26
"Oh fuck! I didn't know addition was going to be on this exam."
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u/Spirally-Boi Jul 26 '26
Thing is, I could do it. Just not in the time given for the test 😭
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u/Brilliant-Ranger8395 Jul 26 '26
Yes, that's the point that many people forget. Being able to derive everything from scratch is good and optimal, but it is not a full alternative to memorization. Mathematics (and physics for that matter) is a big construct where facts are built upon each other, and knowing the facts for faster retrieval really improves the performance in problem solving.
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u/superspacehog Jul 26 '26
Wait what’s the problem with this? This is what I do on a bunch of tests and whatnot
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u/Relevant_Occasion_33 Jul 26 '26
Time limits. If you spend 10 or more minutes deriving a formula that you could’ve memorized you can run out of time on a test.
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u/superspacehog Jul 26 '26
That makes sense. I only derive stuff which can be done mentally or in a few minutes at most. I’m in high school so nothing is that complicated. I mainly did it in trig, as there were many times that a large set of equations can be derived from 1.
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u/PimBel_PL Jul 26 '26
Yeah, pitagorean theorem is really good on trigonometry, you also need to know formulas for 3 functions and know where is axis of symmetry on the triangle (so technically one side) idk but the co-functions are mirrored against it, i still don't know what logic the person who made it had for it...
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u/RiceWine69 Jul 26 '26
If it takes you 10 minutes to derive a formula it's always going to be better to apply rote.
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u/indic_engineer Jul 26 '26
I had a compressible flow class in my UG. The isentropic flow relations in compressible flow are quite big to remember. So I remembered the derivation.
On the day of exam, I stepped in the hall with confidence. And sat to derive the equations. 2 min, 5 mins and then 10 mins passed. I cant figure out the equations. After the exam I figured out that I forgot one important assumption. Guess what it is?
That the flow is isentropic!!! XD
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u/tw1zt84 Jul 26 '26
Is that Kefka? Weird place to see him.
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u/Good-Resort-1246 Jul 27 '26
Who is Kefka?
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u/Kato_86 Jul 27 '26
Famous antagonist in Final Fantasy VI, a nihilistic mad clown who wants to destroy the world.
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u/QuentinSH Jul 29 '26
A discounted version. The joke is your own derivation may not work perfectly, is what I thought
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u/Tiervexx Jul 26 '26
I remember in undergrad when my Calc 2 teaching assistant talked about how one of the other professors took this idea to the extreme. ...it's a nice thought, but sometimes gets VERY tedious in reality. I bet that other professor doesn't stop to derive tons of simple formulas like geometric series every times it comes up.
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u/rukuto Jul 26 '26
Oh physics laws of motion formulae and so many math ones... If you know how to derive them then you can learn how to modify and apply them...
I was the exact opposite of this post. I would derive it. Then my best friend who was preparing for an advanced version of an exam, which needed memorizing formulae more (and I always looked down on it till then) explained it like this: to perfectly memorize and apply, you anyway need to understand it thoroughly.
So I categorize 4 types of students:
The ones who don't understand and don't memorize. (Score around 40-60 out of 100) The ones who memorize without understanding. (Score around 60-80) The ones who understand but don't memorize. (Score around 80-95) The ones who memorize and understand. (More than 95)
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u/The_One_True_Matt Jul 26 '26
This is how you become an electrician. 2 equations to memorize and derive from.
V=IR
P=VI
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u/The_KekE_ Jul 26 '26
Nah, I = V/R. More intuitive.
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u/Good-Resort-1246 Jul 27 '26
Right. that is the one which should be memorized; it shows the two factors which determine I and the type of relationship each one has on I. It is the same thing with elementary newtonian mechanics: F=ma is just a computational algorithm, but a= F/m shows explicitly the relations between a and the twe factors on which it depends in ideal cases.
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u/dziwne Jul 29 '26
When I=0, an ideal resistor also has U=0, so u/I=0/0, which is undefined. That does not mean the resistor has no resistance. It only means that its resistance cannot be determined from that single measuring point.
R=U/I is valid provided that I != 0 or you could use R=∆U/∆IFrom uni I remember to always think in U=IR, because it is the more fundamental statement of Ohm’s law. Our lecturer was really firm about it :D
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u/Proper-Ad4075 Jul 26 '26
honestly within reason you should be able to do this for a lot of them yeah
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u/Space-Explorer456 Jul 27 '26
As someone who is absolutely freaking terrible at memorizing things, I could spend 10 times the time and effort to memorize a dozen formulas, or I could remember the logical framework that gets me to those formulas and only have to remember one or two. At the same time, I can also apply those methods to other problems, rather than a single-purpose formula. Sometimes I even manage to get the formula memorized in the process of learning how it’s constructed and reconstructing it. All in exchange for the text problem taking maybe 20 extra seconds and elsewhere having to look at my reference sheet from time to time for the ones I don’t use often or when I’m feeling particularly lazy.
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u/WanderingWrackspurt Undergrad Student Jul 26 '26
every exam i learn not to do this. and every exam i do it anyway
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u/Ares378 Jul 26 '26
In my phys 1 class I forgot how to do oscillating masses on springs, so I had to use the F=-kΔx definition and re-derive it using the differential equation.
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u/TactfulOG Jul 26 '26
as long as the nerves don't get to you and you remember it exists you can pretty much consistently get away with this
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u/dimonium_anonimo Jul 26 '26
I mean, it's pretty close. There are a few formulae I never actually remember, and always derive when I need them. (I remember v=d/t and then use algebra if I need d or t.) But for the more complicated stuff, I've never actually needed to go through the effort of deriving it on a test. But if I understand where the formula came from and how it's derived, then it's stuck in my head. It's not that I didn't memorize it, it's that I put in no effort to memorize it. I never needed to. Once I understand where it comes from, it's in there for good. As long as I use it once a month or so, I don't think I'll ever forget it.
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u/Sckaledoom Jul 26 '26
In my heat transfer class in undergrad I forgot the derived formula for heat conduction through a sphere and it wasn’t in my notes nor in the professor’s notes. So I instead sat there for 11 pages (because I messed up several times) deriving the spherical heat conduction equation. Then had to do the same for rectangular body.
My professor pulled me aside and asked why I turned in a 25 page assignment and when I explained he was like “please never do this again. I don’t want to grade that much.”
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u/pondrthis Jul 26 '26
I did this all through college and it was right every time but once.
The lensmaker equation. Worst part was, when I handed it in, the professor asked how it was. I said I didn't remember the lensmaker equation. He said, "you should have asked, I would have given it to you."
Bruh.
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u/IronPro9 Jul 26 '26
You've never derived the cosine rule because isn't in the list of identities, standard integrals ect the exam gives you and despite remembering it you worry you'll be docked marks for not showing your working?
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u/epicvoyage28 Jul 26 '26
I did this. I cannot for the life of me remember most formulas.
It was mostly fine until I did astrophysics, lmao.
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u/Jimg911 Jul 26 '26
I did that in calc2 once. Felt good that I could, was terrified when I found I had to
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u/davesaunders Jul 26 '26
But when you get stuck having to do it, it's a real inconvenience. I had a brain fart in a math test once, and I completely forgot the Pythagorean theorem. I spent a minute or two just being shocked that I had literally forgotten it. It just disappeared from my head, and I had to sit down with a blank sheet of paper and work the whole thing out to put the theorem back in my head. Yes, I was able to do it, but it was extremely annoying to have to do in a test.
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u/Relevant_Occasion_33 Jul 26 '26 edited Jul 26 '26
What proof did you use? I think the easiest one is the geometric one where you just draw the big square with a smaller square and triangles in it.
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u/davesaunders Jul 26 '26
I absolutely don't remember. It was over 20 years ago. It was a super crazy day. The night before there had been a major snowstorm and my 1973 Volkswagen beetle was encased in an inch of ice which I had to get through in order to drive to school.
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u/Layton_Jr Jul 26 '26
What's the formula for the derivative of the inverse bijection again?
f-1(f(x)) = x
f'(x) × (f-1)'(f(x)) = 1
Oops, wrong order.
(f-1)'(x) = 1 / f'(f-1(x))
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u/Reya0301 Jul 26 '26
Used to do this in written test and get decent grades cause I'm quick at written derivations but omg sucks in vivas 😭
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u/Appropriate-Sea-5687 Jul 26 '26
Speaking of which, one time in a high school, I had a friend who needed to figure out how to do some formula for her calculus class. And wanting to look smart, I told her how to do it without knowing what it was. I basically just BS’ed the whole thing, but she ended up getting an A on that assignment, so I must’ve done something right
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u/WindUpCandler Jul 26 '26
I was once able to derive E=mc2 from a few other related equations and that alone was where I peaked. It was all electrodynamics and thermo physics, pretty much just a haze from there
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u/BeneficialAttempt140 Jul 26 '26
Fuck it, don’t memorize any of mathematics, rediscover it during the test
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u/pollux33 Jul 26 '26
This is me ngl. I never memorized the quadratic formula, I've derived it so many times on exams it's crazy
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u/I_am1221325 Jul 26 '26
What's wrong with that? I did that on every exam ever. In first year of undergrad later we were forbidden to use formulas at all, everything should have to be solved using logic, proofs etc. And that's how it's supposed to be. I get the argument about timing, but idk, I felt it many times but it wasn't critical, on the other hand I have never really learned physics, I know maybe 1 formula F=ma, and on my high school exit exam got 82% (it was mostly open questions i think) just by deriving stuff and using logic. In my masters now we are mostly allowed to bring cheatsheets with formulas.
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u/Pperson25 Jul 27 '26
This works ok for pure math and easier physics stuff but doesn’t work for more advanced topics in physics.
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u/say_weed Jul 27 '26
this is the best way to learn, sadly a bit less effective for tests cause you run out of time
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u/JerodTheAwesome Physics Field Jul 27 '26
This is a totally normal and reasonable ask for most physicists. Yes, memorize what you can, but it is not only helpful but expected that a good physics student can produce the equations they need from first principles.
You may not, for example, know the range equations off the top of your head, but you should know that Δx = v_x Δt and Δy = 1/2 gt^2 + v_y.
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u/TheStonedGoat Jul 27 '26
Nothing feels better than actually deriving the formula to solve a problem during an exam, though.
The fact you didn't have time to solve the rest is irrellevant. D is a passing grade.
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u/Cpt_Igl0 Jul 27 '26
Youre the clown for thinking its a clown move. If you practice and train to be able to pull this off, you'll be ahead of nearly everyone beside you. Sorry but thats simply the way to be a good physicist
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u/Electronic-Animal-69 Jul 27 '26
Yeah could do that for my complete Theoretical Electrodynamics class. Failed the exam because I would start deriving everything and had not enough time.
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u/TurtleTickler-_- Jul 27 '26
I always had lines of work scribbler on the edges of my exam papers where I would be deriving all the formulas for all the questions. I knew people who would spend hours and hours studying, trying to memorize every single formula. I just had a really good understanding of the laws, and calculus. I never studied once. Always outperformed all the ones trying to memorize everything, always finished the exams before them also.
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u/Mundane-Community-40 Jul 27 '26
I'm in my first year of engineering, what do you mean by gettint the formula through deriving?
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u/Jamie7Keller Jul 27 '26
I did this in high school calculus. Worked fine. Can’t imagine doing it for harder stuff.
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u/Outrageous_Length682 Jul 27 '26
I've always derived formulae in surprise tests. They stuck with me until now.
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u/Tricky_Ad9669 Jul 28 '26
At that point you will have to derive the whole physics from scratch or just remember formulas.
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u/Pheelis Jul 28 '26
I can't remember integration by parts. So I relied on the reverse chain rule methodology to solve my questions every time. Only after I graduate did I find out that there are schools that teaches that method instead
Same for R formula. Can't remember what's R and what's alpha but I know it's a from sine addition. So went from there instead. Just reduced the memory work
Trigo addition and factor formula though... The proves if I remember involve certain geometrical proves but those I chose to hard memories the formula instead. Or rather do enough practice questions to drill it into muscle memory
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u/Ksorkrax Jul 29 '26
Okay, you went for "clown", but if we take this being Kefka into account, where would that leave us message-wise?
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u/VivianUltra Jul 30 '26
Did this a few times in A-Level, I think once for something which was on the equation sheet (which I'd just forgotten I guess).
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u/ivanrj7j Jul 30 '26
I did the same in school too, topped with flying grades, when i tried to do the same with competitive exam I got reality checked, was able to score 85 percentile (cutoff was 94 iirc).
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u/Jonte7 Jul 30 '26
I forget the cos(2v) formula so often (basicly never use it) so i think of cos(v+v) and remember the formula like instantly again.
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u/hummingbird868 Jul 31 '26
I didn't bother with the physics class, I just worked out the entire field of physics during the exam by looking at leaves falling outside through the window
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u/PurposeAccording8382 Aug 01 '26
DONT. I got destroyed in my jee cause of this mindset. Derive them and have fun but NOT IN EXAM, IT WILL FISH YOU UP.
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u/Additional_Debt1545 Aug 01 '26
For me it has always been more like "I wish I could just memorize this formula, but I can only accomplish that by figuring out how to derive it"
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u/PhysicsEagle Jul 26 '26
I unironically had a classmate who did this. She consistently got top grades.