0:55 Giving it F tier... It is the method underneath all derivative formulas and you should appreciate it. 2:16 I agree... This all trig stuff is a strange mess and you shouldn't memorize it now because, like... EVERYONE HAS AT LEAST 1 SMARTPHONE AND WE HAVE SPACE FOR ALL THE FORMULAS IN THE WORLD AND GENSHIN IMPACT?
First principles is grossly misused in schools/universities in my opinion. It’s very interesting using it to prove the basic rules of differentiation (power rule, chain rule, product rule and the basic functions, etc). However, using it to find the derivative of lengthy polynomials is such a pointless and immediately trivialised chore. So I can understand why people hate it with their very being. Trig is like e^x, it’s pretty simple at it’s core. All you need to know is the derivative of sin and cos, and use other rules to work out the derivatives for the other functions. Memorising a formula sheet, while it might save you some time, involves more effort than it saves.
@@gregstunts347 yea first principles just gets confusing for a lot and they will only use it for a few times and probably wont touch it again. its not hard but people just forget it ig.
@@gregstunts347 i agree, the definition of derivative should be used to teach the proofs to the common patterns we see as the chain rule etc and for trig derivatives i disagree you can definitely time by just memorizing the trig derivatives as they aren't that complicated and are easily memorizable which take a good minute to derive which you would need on a test and in the real world who's gonna be memorizing any math💀just use an online calculator
Honestly it is. Like, I barely passed middle school maths, and the stuff I learn at mechanical engineering isn't that difficult to me. I still don't get "good" grades, but I can understand what is going on.
trig derivatives aren't "just memorization" besides what memorization you'd already done for trig class. all you need is sin -> cos -> -sin, and the rest come straight from that and the other rules and even that, you don't need to memorize, if you know euler's formula, e^ix = cos(x) + i sin(x). because then you can separate out cos as (e^ix + e^-ix)/2 and sin as (ie^-ix - ie^ix)/2 and even the basic sin and cos derivatives fall out from the chain rule
Yes, but that takes time. Can't afford to do that. I had solved a physics problem using the thing u described because i didn't know or for some reason couldn't differentiate normally.
logarithmic differentiation? a variable to the power of another variable derivative of x^sinx are solved in order by Chain rule Exponential Derivatives and Derivative of sine answer is lnx•(x^sinx)•cosx
slight correction rewrite x^sinx as e^(x•ln[sinx]) let xlnsinx as u d/dx e^u = e^u du replace u and du with the correct functions du=ln(sinx)+x(tanx) actual correct is ln(sinx)x^(sinx)+(tanx)x^(sinx+1)
Even if you don't like the def of derivative (me too), at least give it respect because without it, those formulas wouldn't be a thing. Think of it like this: You have to respect your parents even if you don't like them because you wouldn't be here if it weren't for them
They are so complicated to normal people so they never teach Gamma funct. or Lambert W in most schools unless you are studying in a field that makes use of them often.
This is only a derivatives tier list and lebesgue integrals are a form of integration which is primarily used when either the Riemann integral is not defined for our function and mainly we use lebesgue integration to show that our function is integrable, because no one cares about computing hard integrals just that the integral does exist. Or it is used on spaces with different measure like probability spaces.
@@Kcl-Integrator29 Just wanted to make a sarcastic joke. I would never consider to study mathematics. NEVER!!! I‘m not a math student im just casually interested in math. Im going to start engineering in a few months.
Trigonometry is the best I see the trig-identities big number as a quality, a way that relates many fields in math, has cool and useful applications and of course a beauty at it's own
I would put quotient rule at D simply because you can just rewrite expressions into product rule format, which is much easier and order doesn’t matter for product rule.
I don't know about y'all but I'd rank Quotient Rule over Product Rule. The Product Rule is just full of factorisation, which is absolute pain when you have to differentiate 3 different kinds of functions [x'•y•z + x•y'•z + x•y•z']. Even in fraction, you're basically adding an additional step, converting the fraction into a negative power, and then another step with bringing it back down when you're done.
3:17 no product rule Is SSS tier. It Is in fact so important that when you go to manifolds and differentiable geometry this Is how you create a abstract definition of a derivative, that different from other linear operator d(x*f)=d(x)*f+x*d(f) ( or d(x*f)=d(x)*f-x*d(f) the signal part Is too long to be explained In a youtube comment ).
im procrastinating right now by watching this video yet i have a derivative test in two days and currently on break after studying for an hour. am i procrastinating or studymaxxing
The only thing i disagree with is the quotient rule rank, because it's actually a great technique,as great as the product rule The only problem is that less careful people might forget to take restrictions, although that's pretty much highschool math
You are wrong about what you call the "first principle of derivatives". Not only is it used to prove all the other differentiation techniques, there are functions that can't be differentiated using the other techniques in which case you might need to use it directly.
@@Kcl-Integrator29 tbh, I'm mostly just bitter after an exam. If you put the time into it and try to understand the proofs (I suggest cross referencing), you'll be fine.
Should’ve separated out sin and cos from the other trig functions. They’re an easy A tier ranking. I don’t even bother with the table of trig functions, just use sin and cos with the product/quotient rule. First principles should be a B tier topic, but with the way it’s taught, it is an F tier topic. It should only ever be used to prove the basic rules of differentiation. Instead, it is used to manually differentiate functions that would normally be extremely trivial to do so.
If your teacher / prof is making you memorize trig derivatives then they are doing it wrong You’ll usually know the sine and cosine ones by heart and the other ones like never come up after calc 2
feel like chain rule should be s tier because it comes up so much even for single variable its used for pretty much every function if the argument is a multiple of x
@@Kcl-Integrator29 damm i just looked into your channel , im exactly the same as you , just wrote my 2nd sem exams 10 days ago , going to 2nd year in aerospace engineering. all the best.
@@Kcl-Integrator29 idk , its not decided by my , its determined by my university . i think i get to pick some optional courses only from my 3 year im not sure , ill let you know once i get it , but i got the curriculum for 2021 batch and i had the same courses in my 1 st year (but the courses were a bit shuffled up in my 1st n 2nd sem , but same credits tho) ill post a screen shot through a discord link.
@@Kcl-Integrator29 bruh youtube is deleting my comments if they have a link in them. , what courses do you have for next sem ? i think my classes will start from july 15th
What I'm doing here? I'm just ended 8th grade where we just learned about quadratic equasions and linear inequalities and ended up watching a video about calculus. How?
@@Kcl-Integrator29 Begginings of calculus start in 10th grade, if I not being mistaken. But I surely will go to the math or IT facultet, so early calculus knowledge certainly will be useful
youre such a baby if you think memorising trig derivatives/integrals is hard ☠did math end at 13x12 for you or is that too difficult and should be left to your phone too
![[UNCUT] The Loyal Pin ปิ่นภักดิ์ EP.15 (3/4)](http://i.ytimg.com/vi/IVwR87OH0_A/mqdefault.jpg)
If anyone has any videos or tier lists you wanna see just lemme know
Indeterminate form (limit function) tier list
Will start a script soon. I have some plans for some new videos within the next month
bro forgot the e^x the most god-tier level derivative there is
ye, fr
I got it in my functions tier list
Not if you’re a programmer
If you’re a programmer exponential=death
@@NathanSimonGottemer depends on the exact circumstances i'd say. Which one do you have in mind?
I forgot e^x our saviour 😔
That's in S Tier
I even use the e^ln method instead of the logarithm method because frankly it makes more sense to me
@@AlvinFS27 do you mean S++++++++++++?
@@savitatawade2403 I think it is in the U(ultra) tier
@@theoneeditor399 O tier (omega)
This is the most engineer video of all time!
0:55 Giving it F tier... It is the method underneath all derivative formulas and you should appreciate it.
2:16 I agree... This all trig stuff is a strange mess and you shouldn't memorize it now because, like... EVERYONE HAS AT LEAST 1 SMARTPHONE AND WE HAVE SPACE FOR ALL THE FORMULAS IN THE WORLD AND GENSHIN IMPACT?
First principles is grossly misused in schools/universities in my opinion. It’s very interesting using it to prove the basic rules of differentiation (power rule, chain rule, product rule and the basic functions, etc). However, using it to find the derivative of lengthy polynomials is such a pointless and immediately trivialised chore. So I can understand why people hate it with their very being.
Trig is like e^x, it’s pretty simple at it’s core. All you need to know is the derivative of sin and cos, and use other rules to work out the derivatives for the other functions. Memorising a formula sheet, while it might save you some time, involves more effort than it saves.
@@gregstunts347 yea first principles just gets confusing for a lot and they will only use it for a few times and probably wont touch it again. its not hard but people just forget it ig.
@@gregstunts347 i agree, the definition of derivative should be used to teach the proofs to the common patterns we see as the chain rule etc
and for trig derivatives i disagree you can definitely time by just memorizing the trig derivatives as they aren't that complicated and are easily memorizable which take a good minute to derive which you would need on a test
and in the real world who's gonna be memorizing any math💀just use an online calculator
Genshin Impact really impacted my grades
@@pythonprogrammers3597 I guess you could say, it Genshin Impacted your grades
When you think about it, mathematicians think engineering is middle school level difficulty. 🤣
Honestly it is. Like, I barely passed middle school maths, and the stuff I learn at mechanical engineering isn't that difficult to me. I still don't get "good" grades, but I can understand what is going on.
I've been waiting for this , good work!
Do you have any other video requests?
@@Kcl-Integrator29 math formulas maybe? Idk im out of ideas lol.
@@Kcl-Integrator29 do for differential eqn or coordinate geometry
both suck with formulas
trig derivatives aren't "just memorization" besides what memorization you'd already done for trig class. all you need is sin -> cos -> -sin, and the rest come straight from that and the other rules
and even that, you don't need to memorize, if you know euler's formula, e^ix = cos(x) + i sin(x). because then you can separate out cos as (e^ix + e^-ix)/2 and sin as (ie^-ix - ie^ix)/2 and even the basic sin and cos derivatives fall out from the chain rule
Yes, but that takes time. Can't afford to do that. I had solved a physics problem using the thing u described because i didn't know or for some reason couldn't differentiate normally.
even those two are unneeded
@@ChromaticPixels technically, sure, but they're so simple and common that you might as well know them
We got derivatives tier list before GTA VI
The tier list looks like an E that’s how much of a god tier e^x is that it overshadows everything else
logarithmic differentiation? a variable to the power of another variable
derivative of
x^sinx
are solved in order by Chain rule Exponential Derivatives and Derivative of sine
answer is
lnx•(x^sinx)•cosx
slight correction
rewrite x^sinx as
e^(x•ln[sinx])
let xlnsinx as u
d/dx e^u = e^u du
replace u and du with the correct functions
du=ln(sinx)+x(tanx)
actual correct is ln(sinx)x^(sinx)+(tanx)x^(sinx+1)
Even if you don't like the def of derivative (me too), at least give it respect because without it, those formulas wouldn't be a thing. Think of it like this: You have to respect your parents even if you don't like them because you wouldn't be here if it weren't for them
before you know it, they are peddling the Gamma function
and then randomly decide that the Lambert W Function is the greatest thing since sliced bread
They are so complicated to normal people so they never teach Gamma funct. or Lambert W in most schools unless you are studying in a field that makes use of them often.
truest implicit diff take Ive ever seen W list
Soooo….
What about real analysis or lebesgue integrals???
We do not tolerate math students around here
@@Kcl-Integrator29 The only right opinion
This is only a derivatives tier list and lebesgue integrals are a form of integration which is primarily used when either the Riemann integral is not defined for our function and mainly we use lebesgue integration to show that our function is integrable, because no one cares about computing hard integrals just that the integral does exist. Or it is used on spaces with different measure like probability spaces.
@@Kcl-Integrator29
Just wanted to make a sarcastic joke. I would never consider to study mathematics. NEVER!!!
I‘m not a math student im just casually interested in math. Im going to start engineering in a few months.
I watched this during calc class,instead of taking notes. Dope video, but I’m blaming you if I fail my quiz.
What about the inverse function rule? derivative of f`¹(x)=1/(f'(f`¹(x)))
I just forgot that was a thing
But if you forget any of those formulas, only the F tier one can save you!
Wheres total derivative, covariant derivative, frechét derivative, Lie derivative, functional derivative, weak derivative?
Trigonometry is the best
I see the trig-identities big number as a quality, a way that relates many fields in math, has cool and useful applications and of course a beauty at it's own
I think it's wrong to put implicit differentiation so low. So many things in the real world use optimization
I would put quotient rule at D simply because you can just rewrite expressions into product rule format, which is much easier and order doesn’t matter for product rule.
I don't know about y'all but I'd rank Quotient Rule over Product Rule. The Product Rule is just full of factorisation, which is absolute pain when you have to differentiate 3 different kinds of functions [x'•y•z + x•y'•z + x•y•z']. Even in fraction, you're basically adding an additional step, converting the fraction into a negative power, and then another step with bringing it back down when you're done.
I liked when you put first principles in f tier
3:17 no product rule Is SSS tier. It Is in fact so important that when you go to manifolds and differentiable geometry this Is how you create a abstract definition of a derivative, that different from other linear operator d(x*f)=d(x)*f+x*d(f)
( or d(x*f)=d(x)*f-x*d(f) the signal part Is too long to be explained In a youtube comment ).
We don’t do that in engineering😊
as someone who just started calculus and only knows the second rule i feel offended but fair enough
trig derivatives don't require memorization; you can derive them geometrically and then understand where they come from
logarithms are actually cracked tbh
im procrastinating right now by watching this video yet i have a derivative test in two days and currently on break after studying for an hour.
am i procrastinating or studymaxxing
2:26 shouldnt it be 1/2 not 2?
The only thing i disagree with is the quotient rule rank, because it's actually a great technique,as great as the product rule
The only problem is that less careful people might forget to take restrictions, although that's pretty much highschool math
You are wrong about what you call the "first principle of derivatives". Not only is it used to prove all the other differentiation techniques, there are functions that can't be differentiated using the other techniques in which case you might need to use it directly.
logarithmic derivatives being in D tier is a huge crime
My rational is solid
Oh boy, he is so going to love differential equations.
(I am losing my mind)
I've only done linear and separable differential equations and I'm not looking forward to the rest
@@Kcl-Integrator29 tbh, I'm mostly just bitter after an exam. If you put the time into it and try to understand the proofs (I suggest cross referencing), you'll be fine.
Should’ve separated out sin and cos from the other trig functions. They’re an easy A tier ranking. I don’t even bother with the table of trig functions, just use sin and cos with the product/quotient rule.
First principles should be a B tier topic, but with the way it’s taught, it is an F tier topic. It should only ever be used to prove the basic rules of differentiation. Instead, it is used to manually differentiate functions that would normally be extremely trivial to do so.
What about exponent rule? (a^x)
its literally in the video
he forgor
@@pechkurofffI'm pretty sure he only did x^x not a^x
I forgor
Cool video! Love the graphics! ❤ 😂
Thank you! :D
what about integrals tier list? btw, great vid
Made an integrals tier list a bit ago, th-cam.com/video/Fp71_1aeVRA/w-d-xo.htmlsi=2V0N8-KxNsPk31jG
If your teacher / prof is making you memorize trig derivatives then they are doing it wrong
You’ll usually know the sine and cosine ones by heart and the other ones like never come up after calc 2
Why would you need to memorize it, can just derive them pretty easily
feel like chain rule should be s tier because it comes up so much even for single variable its used for pretty much every function if the argument is a multiple of x
My math teacher had us doing the first principle of derivatives in algebra 2😕
The ones you rated negatively ,do you have any better ways then ?
The ones in S A or B tier
bro is not a mathematician 😭
Indeed
As a high school sophomore, what foreign language are you speaking
4:13 seems logical to me
pls make differential equations tier list
Taking differential equations this fall then I'll make a tier list
what grade are you in ? or what semester are you in university ?
Going into second year university
@@Kcl-Integrator29 damm i just looked into your channel , im exactly the same as you , just wrote my 2nd sem exams 10 days ago , going to 2nd year in aerospace engineering. all the best.
Good luck fellow aero! What courses are you taking next semester?
@@Kcl-Integrator29 idk , its not decided by my , its determined by my university . i think i get to pick some optional courses only from my 3 year im not sure , ill let you know once i get it , but i got the curriculum for 2021 batch and i had the same courses in my 1 st year (but the courses were a bit shuffled up in my 1st n 2nd sem , but same credits tho)
ill post a screen shot through a discord link.
@@Kcl-Integrator29 bruh youtube is deleting my comments if they have a link in them. , what courses do you have for next sem ? i think my classes will start from july 15th
do one of this but for differential equations
Taking differential equations this fall then I'll make a tier list
Trig derivative should be in S teir in physics it as more applications
0:51 sorry, it's me..., hehehe.
so true brother
Lmao the limit one is actually the best, maybe you are not far enough in calculus to understand why but I promise it is
I guess you get some ungodly functions later on.
@blackpenredpen please make one as well!
My least favorite: inverse trig derivatives. I mean, how do you expect me to actually memorize those and keep remembering them?
derivative of tan inverse makes more sense when you think of it graphically to me
treating y as you'd treat theta lets you geometrically derive all of em
erm sir, at 0:02 [x] (GIF) is actually non differentiable 🤓☝
damn no del??
No
you forgot about google
reciprocal rule
yes
e^x is the best you monster for forgetting of it why...
IMPLICIT DIFFERENTIATION IS AT LEAST A TIER HOW COULD YOU SAY OTHERWISE
when the funny ahh video you found on youtube is more useful than your math teacher:
3:48 [f(x)^((g(x))]'=[f(x)^((g(x))]{[ln(f(x))g(x)]'}
loved the video but the biology slander... 😞
sorry :(
you hella funny bruh you earned a subscriber
not me tho
i actually like trigonometry derivatives.. I love memorizing stuff and being able to use it
God will not show you any mercy.
@@anjanavabiswas8835 😭
understandable though i disagree -- if you're interested though you can understand it intuitively
Hey man... memorizing is cool. 😢
no :|
What I'm doing here? I'm just ended 8th grade where we just learned about quadratic equasions and linear inequalities and ended up watching a video about calculus. How?
Getting prepared. When do you take your first calc class?
@@Kcl-Integrator29 Begginings of calculus start in 10th grade, if I not being mistaken. But I surely will go to the math or IT facultet, so early calculus knowledge certainly will be useful
Good luck! Make sure you practice and fully know how to factor. Factoring is really important for your next few years of maths
also just just derive trig dertivatives so you don't have to memorize them.
Too lazy
i use the f-tier derivatives to find the f-tier derivatives
yep limit definition@@kaito383
0:11
although no one asked but this is not a polynomial
Hence the hee hee hee haw clash royale emote
@@Kcl-Integrator29 🥺
youre such a baby if you think memorising trig derivatives/integrals is hard ☠did math end at 13x12 for you or is that too difficult and should be left to your phone too
Who hurt u bro 💀
I will not tolerate trig slander! What’s to memorize about sin’s derivative being cosine? They’re all pretty intuitive if you ask me.
No
e^x 😢😢😢