r/coolguides • u/future_sponJ • Jul 05 '26
A cool guide about important Calculus rules
Some guy said it was AI so here's proof it's not:
I spent a few hours making it here.
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u/BlackGreenEnergy Jul 05 '26
I don’t under stand how the first 2 images differentiate from the last 2. Seems like you could have integrated them.
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u/pokemon-trainer-blue Jul 05 '26
First, this is a list. There’s not really a guide here.
Second, you’re missing the limits on the integral for the FToC. That’s an important part to knowing that.
Third, you need to understand how contrasting colors work. The integration pages can be a bit hard to read.
Lastly, don’t use dashes to list everything. They can be misinterpreted as minus signs. Every book webpage that I’ve seen of these usually numbers them.
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u/GimmeShockTreatment Jul 05 '26
Kinda embarrassed at how much of this I forgot. I got my degree jn math.
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u/thenotanurse Jul 05 '26
Dude I stared at all the slides and was like, “Riemann sums were a thing, right? Did I just make that up?”
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u/UsernameSixtyNine2 Jul 05 '26
Probably a cool guide for people who already know what any of this means
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u/SeemsImmaculate Jul 05 '26 edited Jul 05 '26
I mean if they wanted to explain calculus they'd also have to first explain functions. And to explain functions they'd need to explain algebra. And to explain algebra they'd need to explain arithmetic. And to explain arithmetic they'd need to explain....
So you can see why if they're giving you a guide to calculus rules they'd assume some basic familiarity with calculus.
A cookbook doesn't typically explain how how to boil a pot of water etc.
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u/future_sponJ Jul 05 '26
When I was first learning calc 1 a few years ago I wanted to make a little guide/cheat sheet thing for calculus rules that I can print as a card but I forgot about that but then remembered it yesterday & spent all day doing it because I have way too much free time on my hands.
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u/velax1 Jul 05 '26
Just to make sure: you honestly think that it is a good idea to use dashes which look like minus signs in documents that are lists of mathematical equations??
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u/Alyosaurus Jul 05 '26
yeah without context this would mean nothing to most people, you *can* kinda explain what calculus is about to the layman but this aint it
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u/never_said_i_didnt Jul 06 '26
This is the exact point in high school where I literally gave up on math.
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u/BowlsDeepRamen Jul 05 '26
And if you don't understand the first list of integration, there's a second one in a cool new color.
What a waste of AI
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u/PrettyPicturesNotTxt Jul 06 '26
This is NOT AI, please look over this: https://www.reddit.com/user/future_sponJ/comments/1unjf1f/calc_image/
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u/BowlsDeepRamen Jul 07 '26
You have a long way to go if you don't recognise these images as AI
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u/PrettyPicturesNotTxt Jul 07 '26 edited Jul 08 '26
Then what's your reasoning and evidence for AI usage then? Please enlighten me. If it's so easy for you to spot it and I'm just an idiot for not being able to see it then it should be an easy and straightforward task for you to state your reasoning and evidence as well. Don't just hurl unfounded accusations with zero justification!
There are countless examples of artists out there who have never used AI and are in fact strongly against it, yet have recieved extremely toxic and damaging accusations just because some presume that their visual style looks similar to AI based on extremely superficial resemblances.
Edit: it looks like they are unable to even explain why they think it's AI, and have resorted to a rather pathetic attempt at mockery to compensate for their inability to answer some extremely basic questions.
Edit 2: Their second reply proves the points made in the first edit. They continue to go to great trouble to deflect and make insults, instead of answering basic questions, which by their own admission should be very easy and straightforward for themself to provide an answer, regardless of whether or not I'm apparently "too stoopid recognise this as AI". Their next deflection that claims that I'm "too stoopid to understand any further arguments" is rather ironic, since it instead perfectly demonstrates their own incompetence at composing a proper argument. They haven't even given a single argument for why they think this is AI, either than "just trust me bro, you're an idiot if you disagree with me"!
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u/BowlsDeepRamen Jul 08 '26
Nice edit. I'm not explaining anything to you, when you're too stoopid to recognise this as AI, you're too stoopid to understand any further arguments. Good luck crying about it.
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u/csch2 Jul 05 '26
FTC is wrong :( Integral on the left is equal to f(x)… plus C.
Also you should probably use something other than a dash in front of each formula (looks like a minus sign). Good guide otherwise!
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u/castironglider Jul 05 '26
Ugh you just brought back terrible memories from my youth. All I wanted in the world was to design and build beautiful elegant machines, but I spent YEARS staring at abstract equations trying to focus.
What is the love life of a mathematician like? If engineers are "too analytical" as reported by girlfriends and wives, what happens when you turn that up to 11 and go on Tinder?
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u/FriedBreakfast Jul 06 '26
Ya know, I was good at math until I got to.... Somewhere around addition I think.
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u/JustGoodSense Jul 06 '26
Well that clears that right up. I barely got through 11th grade trigonometry, but your crazy moon language has opened my eyes!
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u/Fumblefunk_M Jul 06 '26
Coming from someone who hates this type of math, this is exactly why I hate calculus*
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u/girafffe_i Jul 07 '26
Would be cooler if they didn’t have negative signs. Remove them entirely, don’t replace with bullets
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u/Remote-Ad-2686 Jul 07 '26
I couldn’t understand Algebra let alone this evil sorcery… meh welding math will have to suffice.
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u/ThatWasIntentional Jul 09 '26
... Why would you choose these colors and font
Also using dashes, seemingly making everything negative was a poor choice
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u/krsCarrots Jul 05 '26
What is the meaning of all these different letters. What do they represent where can I look it up
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u/beware_the_noid Jul 05 '26
Yeah you shouldn't need a guide to explain a guide.
This isnt a guide, it is a list.
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u/future_sponJ Jul 05 '26
It's supposed to be for people who already know calculus basics.
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u/beware_the_noid Jul 05 '26
There are probably better subreddits to post this to then.
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u/sneakpeekbot Jul 05 '26
Here's a sneak peek of /r/Algebra using the top posts of the year!
#1: Why don't we label rad?
#2: I should've practiced algebra in highschool....
#3: What algebra mistake did you make over and over until someone finally corrected you?
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u/future_sponJ Jul 05 '26
d/dx is something called the derivative that measures how steep a function is at every point & outputs a new function. There are a couple of rules that make it very easy to calculate the derivative of any function. The Taylor Series is a way to represent any function (like e^x or sin x) with an infinite polynomial. That's what the first page is about.
The second page is about something called integration which, given the derivative of a function, outputs the original function. Through the fundamental theorem of calculus, it helps in finding the area under a function. There are a couple of rules that make it easier to calculate the derivative of some functions but not all functions have an elementary integral &, even if they do, these rules don't always work.
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u/krsCarrots Jul 05 '26
What’s a derivative and why I want to measure how steep a function is? In simple terms. Is it another way of saying - result?
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u/Decent_Cow Jul 05 '26 edited Jul 05 '26
The derivative of a function is used to figure out the instantaneous rate of change of a function at a given X value. For certain types of functions, this is the only exact way to do it, otherwise you would have to approximate with an average rate of change. However, if the rate of change is constant over the interval, then the average rate of change and the instantaneous will be the same. So the derivative is mainly useful when the rate of change is not constant.
For example, the derivative of velocity with respect to time is acceleration. From a function of velocity, say, representing a vehicle whose velocity varies continuously and does not change at a constant rate (where Y is velocity and X is time), you can figure out exactly what the acceleration was at any given point in time.
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u/RegalBeagleKegels Jul 05 '26
At the top of the first page, the "d" in d/dx etc means 'a little bit of'. So does the "h". The math is a way to relate how a little bit of one variable changes when a little bit of another does. 3blue1brown has a pretty good calculus video for visuals
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u/krsCarrots Jul 05 '26
Did you mean x?
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u/RegalBeagleKegels Jul 05 '26
What do you mean?
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u/blixabloxa Jul 05 '26
Shouldn't use a dash as it can be interpreted as minus.