I've had a few cycles where I learned calculus,then forgot it, then learned it again, then forgot, etc. With time, the 'easy tricks' disappear, and the hardwired core of knowledge stays with you. So, if you spend your time memorizing huge numbers of little tricks, expect them to be gone in a year. What really gets you into trouble is partial memory, which has to be perfect if you rely on memorization. Better to understand the fundamentals, following the pattern of classical teaching, and burn those core fundamentals into your long term memory. For example, rather than memorizing all the trig substitutions, learn Euler's formula and derive the one you need with a few pencil strokes. Little tricks make you faster and might help with the time pressure of an exam, but fundamentals will carry you much farther over the long term.
If you're going to use math for several years, the best strategy to remember it all is to teach it and keep resources you can consult at a glance to jog your memory. It will force you to consolidate your knowledge. All of the quick tricks are useful to compile into sheets to review for posterity while ALSO memorizing the fundamentals in case you are caught unaware and need to prove results from scratch. Using both is the key for efficiency. If you're using math in academic settings as either a student or instructor, you need to have the material at your fingertips and not rederive a myriad of formulas all of the time when you need them on the spot as everything is timed.
None of these is just memorization. They are each provable but then the point of memorizing derivative formulas is so that you don't have to write the proof everytime you compute the derivative. For the first one if y = sqrt{x} then y^2 = x. Then dy^2/dx = dx/dx => 2y·dy/dx = 1. Therefore, dy/dx = 1/(2y) => d/dx [sqrt{x}] = 1/(2·sqrt{x}). The second formula can be proved by applying the quotient rule to 1/f(x). Finally, any of these can be proved using logarithmic differentiation.
@@liamwelsh5565 We do way more in the way of trig derivatives in our calc classes. The few log ones we often see are in the form Ln(u) where u is some function. Similarly for exponentials: we see e^u ALL THE TIME but other bases like 2, 3, etc not nearly as much.
it helps everyone out. except for indians!. this is too advanced for them... i heard that pakistan has to supply tutors to india to help them learn calculus.
Zangetsu Means except Indians??? We don't need this tricks becz what we thought by our teachers/sir is more understandable. And yes y Pakistan needs to give us knowledge becz my sir is neither from Pak and nor from any foreigner countries it is true that exploring knowledge don't has discrimination between anything of course 😑 you are also thought by some or other person.
It seems like it would use more mental effort, but a few dozen derivatives come up again and again, so if you memorize them, you can quickly finish solving problems, even mentally, without having to rederive specific instances of a derivative after you are no longer being tested on the basic derivative rules. It's also helpful when you are running low on time for multiple choice questions where you don't need to show work.
@@threem1085 I'm not but many people keep saying I'm good. hey, try searching PATRICK JMT on youtube! he generally sums up my 2 hr class in just 20 mins or less. he is the reason why I survived all my calculus when I'm in engineering. Good Luck!
@@threem1085 and btw you need to practice solving a lot of problems. watching and studying vids won't help you but putting it into practice won't betray ur hardwork. you reminded me of myself before xD like I'm really doing well on HS but in college I feel dumb and stupid xD
@@lazypawtato8701 I am a senior in hs struggling so I actually am stupid 😭. I just have two other college classes I'm taking and the work load is just too much. I need make time where I can practice calc other than the packets we get outside of school but man, I'm struggling hard
Our teacher was nice, she told us the first two and I discovered the 3rd myself. I am so pleased to see the thing just pop in my mind in a RU-vid Video.
Actually the last trick was pretty surprising. I`ve thought of using logarithmic differentiation for variables with exponents when it comes to fractions, and apparently it does work. Thanks!
Great tricks. I think that most students who spend enough time doing homework and doing practice problems stumble upon these tricks on their own. For the students struggling with derivatives this could definitely help them get a light bulb moment and hopefully help them spend less time struggling with some of these concepts.
The last one is called logarithmic differentiation. It is a known technique and is taught in Calculus I. Also, those are not tricks, they're the actual methods.
i know that there are a bunch of comments saying that they're disappointed by these tricks, but i found this video extremely helpful. Thank you so much
The last trick cannot be used in all similar cases since you cannot apply logarithms for all real values. In the example you gave the function f(x)=y is defined in (3, +infty) and y is positive so you can apply logarithms in both sides.
Well, I'm not from India, but I agree with what they're saying... this video is pretty much useless and those are NOT "SECRET" TRICKS none teaches at school... probably, they didn't teach you at your school, but they're very well known elsewhere (Europe, India, Russia, etc.)...this video is just clickbait...
L J some 10 years olds from any country can be taught advanced maths stuff like differentiations, matrix, etc. It depends on their faculty for learning, and also their studying habits. I have taught my studying techniques to the weakest students who find themselves jumping to the top in class. I strongly encourage self-teaching in kids and adults. Weakest students lack self-reliance, as they make the mistake of waiting to be told what to study and what not to study, their BIG mistake. Relying on teachers should be 10% and self-teaching 90%. All child prodigies do that.
Thanks for this informative video. You have gotten yourself a new subscriber. Although there are many people calling this a fundamental topic, its not like everyone has this access to this kind of topics everyday. With that, I thank you for your efforts in this video. :) have a nice day
BriTheMathGuy I just love your patience! Although, the tricks were something I figured out myself (and I think everyone should), thanks for making the video. Tip: To make this work better, you could write down the problem and give the viewers some time to figure out the shortcut themselves (this stimulates the mind to think out of the box) and then tell the answers. This way, the viewers might even come out with a newer, better method. After all, mental stimulation is a preliminary requirement for intellectual development. *Hoping to get more exciting stuff from you in future :)*
In French high schools the first two “tricks” are actually proven in class with the definition of the derivative and students are told to memorise them, and in opposition they are asked not to use what you call the “old ways” because the power rule is not proven for non integers at 11th grade. What could be called the reciprocal rule is also taught: (1/u)’=-u’/(u^2) as it is handy for the proof of the quotient rule.
The two first "tricks" are literally how the derivative of a sq root and of the inverse are defined in my high school text book, and for the record I'm *not* Indian. According to my teacher (and I agree), the actual trick is to convert to rational exponent in order to avoid learning more expressions by heart, with the subsequent risk of having a mistake. The third one is , because that expression is quite convenient for the application of the log derivative method. I mean, in real exercises, the polynomial is not factorized s the time you save by logging you waste it finding the roots (if they're rational/it's a 2nd degree polynomial). A real trick would be you can use log derivatives to derivate things like e^(2x^2+3x+1) or 2^x (again, you avoid learning the formula by heart). I saw you also explain the inverse function theorem in another video. I think that actually is a handy trick, along with log derivation.
You are absolutely correct and I won't argue. I simply present these methods since some students prefer them (i.e. more memorization) and some don't. Thank you very much for commenting and all of the feedback. Have an awesome day!
Still useful until 2022,yes the teacher usually will teach the traditional way for solving maths and instead teaching faster way.I am the ones who solve maths at slow pace and I usually got confused when comes to complicated types of questions for maths.Thank you for your useful video.❤️❤️❤️👍👍👍
If you haven't learned the full way to do something, don't 'memorize' stuff! Do it the 'old' way, understand what's happening, then when you do it enough, you won't need to learn trick to do it. And to people saying they learned this, sounds like you didn't learn derivatives, you just learned the 'tricks'.
Correct me if I’m wrong but the power rule is still a trick right??? The ‘old’ way that lets you know what’s happening would be the whole lim h->0 f(x) = f(x+h) - f(x) /h
1:00 So far your tricks to doing derivatives is to just memorize all of them. Good start so far. The problem with the square root, of course, is that it doesnt help with cube roots, etc.
Thanks man I have to learn derivatives (also limits and integrals) in 3 days all by myself without any background at all so this helps a lot for someone who had NO idea of those tricks and NO teacher to teach me at all. Damn it. My diagnostic's tomorrow btw ugh
This tricks are really awesome!, Thank you very much! You're a genius! :D For me, that I haven't started University, this tricks will help me a lot. Thanks!
As someone who has taught Calculus for 20 years, I would never teach the first two "tricks". I believe that the less that a person needs to "memorize", the better. On the other hand, if a student came to me and said, "Hey I found this neat trick!". I would say great. As far as the last one, I DO teach my students to use logarithmic differentiation for problems like that.
1st trick: you could have used the inverse function formula 2nd trick: (1/f(x))'=-f'(x)/(f(x))² You can derive this using a square with area 1 and sides f(x) and 1/f(x)
dude you literally just used the actual method and then you ask us memorise it but anyways i like your positive attitude towards criticism be happy always
Thanks for that last one, it actually helped me understand the use of ln in derivatives, and is a great shortcut. The others I figured out just by doing a lot of derivatives and trying to do them in generic fashions.
Well the first two was just the rules in words 😅. But the now famous last trick is one I use quite instinctively these days. But your video suddenly reminded me of where I first learnt it. And judging by the way you phrased your words, I'd wager so did you. It was Feynman's Lectures or his Tips on Physics.
You have to admit the last one was pretty cool. And I don’t get why you need to drag on a guy for taking the time to put up a video that can help a zillion people (like me.)
@@BriTheMathGuy I honestly thought the video was great, but others (who haven't looked into derivatives or integrals) are here to learn the root of the laws of integrals/derivatives. It's not your fault, I just think they mislead themselves. Great vid, bro!
Chloe Sinéad he expected some secret tricks which will be very useful but got such easy stuff and then he commented ,you can replace that person to me also cos that's what u feel .but these maybe useful for so many people and this guy might help them a lot so he was better from his side it was just us who misunderstood the title
Okay hello this is not where it should be going... Everybody chill.. You come to RU-vid, you watch stuff appreciate someone and you go... that is what it is for.. What you don’t do is fight with other people over a silly thing...and those are the people you don’t even know... So calm down. Everybody has opinions I understand...but keep it to your god damn self.. IF YOU HAVE THE GUTS POST IT ON YOUR CHANNEL!
I mean no offence at all, nice work! However most of us have figured this out already, it takes just a few weeks of practice to do most derivations in your mind itself.....looking forward to other videos. [edit] ok I'll admit your last method was good (the log one), I probably wouldn't have thought to approach the Problem that way!
Brian,chum,the first thing I really tend to tell you is that your videos are incredibly inspiring and illuminating;keep it up,anyway,may I ask you a question?Could you guide me how to take the derivative of some functions which include an expression at the base in terms of 'x' and an expression at the exponent in terms of 'x' as well?
Calculus destroyed me in college. I went all the way through college pre calculus with As, and then got to calculus, the whole Cal I course was solving these long chain derivatives, and I had never seen nor was I able to understand what I was doing or where it was going. My educational system kind of failed me in preparation for this undertaking. SMM…
These are not tricks. This is how you do it when you teach these concepts and you may remember them as formulas if you want. Calling them as trick is not ethical, I guess.
thanks , i had biology till graduation . i never studied math before . yup i had math as additional subject. but i never did pay attention. now in graduation i failed 2 times. now i learned differentiation from yr videos . i m certain i will pass examination this time
