The partial derivative theorem for implicit differentiation is GENIUS. WIth this I can save myself ten minutes + on my A level exam. THANK YOU SO MUCH.
I feel I have seen all of these in your previous videos. Good work as always. Even if I do not use these too much I love to show them to students once they understand concepts to bring things together
As someone that tutors Calc 1 & 2 students these are excellent tricks to help me quickly bypass some of the algebraic mistakes that are made to ensure the right answer has been determined. Keep up the good work with the nice and clear explanations.
@@delarin9276 In my class 12 books they teach all kinds of Derivatives and Integral including a lot of applications of calculus like Maxima & Minima and Differencial Equations. In entrance exams we have to learn all kinds of tricks and techniques for definite, indefinite integrals with extremely hard word problems. In last year of high school we have to learn all kinds in order to get into good college like IITs, NIT and IIITs. Its hell for indian students to get into a good college in india. I was just asking How much they teach in Other Country in Highschool?
@@priyanshumaurya007 they don't teach us that much here in the Philippines, the depth and clarity of learning also depends on the teachers themselves. It also became harder for students to study in college (the college entrance exam is dependent on the school's standards) when the K-12 program was implemented, the program just copied some subjects to grades 11 and 12 then removed "pre-requisite" subjects of major subjects in specific courses. So yeah, the quality of education here in the Philippines is not that very good but not that very bad, just tolerable. That's just my opinion.
You tackle complex problems in the simplest way possible; I love it! Others, llike Micheal Penn and blackpenredpen, race forward, assuming that you are very familiar with and skilled at the content. Of course, Micheal Penn and blackpenredpen are *great*, and I can handle their high speed, but I love how you explain everything!
This was so helpful... Really, big thanks... I have my math final exam in about a month, and casually sitting back and watching few of my videos actually helped me a lot.
I don't know if this is something you mentioned, but another way to phrase trick 2: f'(x)/[square of denominator], times the determinant of the coefficient matrix. In the implicit differentiation trick, once the dust settles, f'= -2x(7x+3)/((x-3)^5).
In the time it takes to recall these 7 tricks you could just differentiate using the standard techniques. These tricks just add more to what you have to remember. (Except for the implicit differentiation trick, which I've never seen before and which looks useful).
How did you film yourself looking at the board, Brian? I would love to know the trick. It seems like you are writing on camera screen. I love the quality of your video and the content of your videos.
The higher order derivative shortcut for the product rule is often taught in mathematical physics courses, which is usually co-listed in mathematics and physics departments and can normally be taken for credit in either department and something both.
Does dy/dx = 1/ (dx/dy) hold true for all functions that are differentiable? Or are there some conditions involved when using this trick, such as availability of inverse functions(one to one relationship), etc? Because I've seen many cases where many cool math formulas don't hold true under certain situations ..... For instance, for this trick, what if we apply it to y = x^2 ? This is a simple function, but if we use this formula, I don't know how it will work because if we write it in terms of x, it is no longer a function unless we divide it into two sections ( x = root(y) or x = - root(y)), whic makes it kind of awkward to differenciate.... How do you apply the formula to these kinds of cases? Thus my question would be, does the equation dy/dx = 1/ (dx/dy) actually hold true for all cases such as this, as long as it's differentiable? How would it be possible for functions that are not invertible (like y = x^2 , y = x^3 - 6x , etc...) I would really appreciate your reply.
This trick is sort just a shorthand notation for the formula for the derivative of an inverse function. So yes - the function would need to be invertible for this to work. (maybe there are special cases to get around this, but in general the inverse is required to exist)
The situation with √x is exactly the same as the situation with arctan x (which Brian used as an example). That is, in each case, to get the inverse function you first have to restrict the domain of the original function so it covers its range exactly once: ]-π/2,π/2[ for tan x and x≥0 for x². The trick worked fine for arctan x and it works fine for √x. I must, however, correct a slip. When Brian said: "y=arctan x x=tan y by definition", what he meant was: "y=arctan x x=tan y where y in ]-π/2,π/2[ by definition".
Superb video to be quicker during exams. Thank you :) By the way, the part where we use Pascals Triangle is coming from Leibniz Formula for those who want to understand why this works.
I don't think the quotient rule should be taught as strongly as it is. Application of the chain rule and the power rule is a lot more instructive and less rote than applying a formula for quotients.
Really believe me the triangle was not invented by Pascal for the first time. He called Khyyam, a Persian Mathematician app 250 year before Pascal who invented the triangle as a coefficient in binominal expansion. Anyhow the triangle is called Khayyam-Pascal triangle to honor both.
well that looks like standard way of doing it with extra steps.Don't get me wrong ,these are nice tricks but knowing product rule and power rule with chain rule is very neat rather than knowing a hundred different rule
These are really useful but there are some problems I can't get the tricks to work with, like ones that would involve multiple tricks. Do these only apply if you can use one trick? Ex: e^(y)cos(x)=1 + sin(xy) Or perhaps I really just don't know what I'm doing. c: I'm tryin' though!
Thank you Brian, I always learn something when I watch your shows. Only one comment, if I may, try not to pronounce the T in the word often. Excellent channel, thank you!
well not all of them sorry i didnt saw the whole video, the second one a teacher told me for integration, third one was given in my book cengage a very renowned book here in india for jee prep
The ad-bc in the 2nd trick looks suspiciously like the formula for the determinant of a 2x2 matrix, is this just coincidence or is there some link between the 2?
Not tricks! These are shortcuts at best, learned from years of use. Kind of how we can decompose equations into various forms to more readily extract information from them, and later extrapolate to a general form, like we do reducing the steps to get and then applying the quadratic formula to get the roots.
Check out all my Math Tricks!
ua-cam.com/video/Ks-wwYpS20Y/v-deo.html
It's amazing how much easier in many ways learning math on UA-cam has become. Pretty cool stuff.
Great to hear!
The partial derivative theorem for implicit differentiation is GENIUS. WIth this I can save myself ten minutes + on my A level exam. THANK YOU SO MUCH.
Pascal's triangle was new to me!! Thanks for the vid 👍👍
Glad you liked it!
I feel I have seen all of these in your previous videos. Good work as always. Even if I do not use these too much I love to show them to students once they understand concepts to bring things together
Yes, I've more or less put many of my videos together in my newer format and for viewer convenience. Thanks very much for all your support!
00:01 - Reciprocal Rule
02:44 - Quotient rule in specific cases
05:24 - Square root functions
08:24 - Implicit functions differentiation
11:40 - Log trick for complex functions with constant powers
15:36 - Higher order derivatives of products
18:47 - Inverse functions trick if we forget
TQ
As someone that tutors Calc 1 & 2 students these are excellent tricks to help me quickly bypass some of the algebraic mistakes that are made to ensure the right answer has been determined. Keep up the good work with the nice and clear explanations.
This video is so helpful. Your rich content is underrated. I hope your channel gets the recognition it deserves!
You're SO helpful!
Thanks very much!
I wish I had seen this channel's contents before going to college
Thanks for saying so! Have a nice day.
Do they not teach derivatives in High School?
@@priyanshumaurya007 the school did but not in depth unlike what the channel taught in the video
@@delarin9276 In my class 12 books they teach all kinds of Derivatives and Integral including a lot of applications of calculus like Maxima & Minima and Differencial Equations. In entrance exams we have to learn all kinds of tricks and techniques for definite, indefinite integrals with extremely hard word problems. In last year of high school we have to learn all kinds in order to get into good college like IITs, NIT and IIITs. Its hell for indian students to get into a good college in india. I was just asking How much they teach in Other Country in Highschool?
@@priyanshumaurya007 they don't teach us that much here in the Philippines, the depth and clarity of learning also depends on the teachers themselves. It also became harder for students to study in college (the college entrance exam is dependent on the school's standards) when the K-12 program was implemented, the program just copied some subjects to grades 11 and 12 then removed "pre-requisite" subjects of major subjects in specific courses. So yeah, the quality of education here in the Philippines is not that very good but not that very bad, just tolerable. That's just my opinion.
I have liked, commented, added to my favorite videos playlist, and shared this video on discord. I love it, and I love what you are doing, Bri!
Thanks for sharing!!
You tackle complex problems in the simplest way possible; I love it! Others, llike Micheal Penn and blackpenredpen, race forward, assuming that you are very familiar with and skilled at the content. Of course, Micheal Penn and blackpenredpen are *great*, and I can handle their high speed, but I love how you explain everything!
I'm happy you enjoyed it! Have a great day!
I just Screenshot all of this. These are so freakin helpful.
This was so helpful... Really, big thanks... I have my math final exam in about a month, and casually sitting back and watching few of my videos actually helped me a lot.
I don't know if this is something you mentioned, but another way to phrase trick 2: f'(x)/[square of denominator], times the determinant of the coefficient matrix.
In the implicit differentiation trick, once the dust settles, f'= -2x(7x+3)/((x-3)^5).
Thanks for a paused explanation, and for not stopping at how to do it, but also naming other cases the tricks help too.
You could also use these as integration tricks if you go the other way
Thank you so much. I'm hoping to take masters in physics and my math is a bit rusty, you helped so muchhh ♡
Really glad to hear it! Have a great day!
please continue to do more videos please you save my life
Thank you so much
Thank you ,you helped me a lot 😊😊
Glad I could help!
the reciprocal rule can be thought of as bringing the power of x to the top by making it negative then using the power rule
im already in calc 3 but i just knew most of these now ! very helpful, thank you
You're very welcome!
In the time it takes to recall these 7 tricks you could just differentiate using the standard techniques. These tricks just add more to what you have to remember. (Except for the implicit differentiation trick, which I've never seen before and which looks useful).
Thanks Bro, you saved my neck in my calculus I exam! :))
Happy to help!
How did you film yourself looking at the board, Brian? I would love to know the trick. It seems like you are writing on camera screen. I love the quality of your video and the content of your videos.
In 1 st he actually used u / v rule of deferential equations
18:34 yes history guy will teach :P , Come to India for battle of jee , thousands of students know it :)
I didn't know that
I salute you sir for your beautiful and wonderful knowledge 💐💐💐💐💐💐🙏🙏🙏🙏🙏🙏
Thanks from Bangladesh..
😊
The higher order derivative shortcut for the product rule is often taught in mathematical physics courses, which is usually co-listed in mathematics and physics departments and can normally be taken for credit in either department and something both.
The shortcut derivative using the reciprocals with respect to y at 18:30 falls out because inverse functions have reciprocal slopes.
Does dy/dx = 1/ (dx/dy) hold true for all functions that are differentiable? Or are there some conditions involved when using this trick, such as availability of inverse functions(one to one relationship), etc? Because I've seen many cases where many cool math formulas don't hold true under certain situations ..... For instance, for this trick, what if we apply it to y = x^2 ? This is a simple function, but if we use this formula, I don't know how it will work because if we write it in terms of x, it is no longer a function unless we divide it into two sections ( x = root(y) or x = - root(y)), whic makes it kind of awkward to differenciate.... How do you apply the formula to these kinds of cases?
Thus my question would be, does the equation dy/dx = 1/ (dx/dy) actually hold true for all cases such as this, as long as it's differentiable? How would it be possible for functions that are not invertible (like y = x^2 , y = x^3 - 6x , etc...) I would really appreciate your reply.
This trick is sort just a shorthand notation for the formula for the derivative of an inverse function. So yes - the function would need to be invertible for this to work. (maybe there are special cases to get around this, but in general the inverse is required to exist)
@@BriTheMathGuy Thank you so much for the answer! :)
The situation with √x is exactly the same as the situation with arctan x (which Brian used as an example). That is, in each case, to get the inverse function you first have to restrict the domain of the original function so it covers its range exactly once: ]-π/2,π/2[ for tan x and x≥0 for x². The trick worked fine for arctan x and it works fine for √x. I must, however, correct a slip. When Brian said: "y=arctan x x=tan y by definition", what he meant was: "y=arctan x x=tan y where y in ]-π/2,π/2[ by definition".
Superb video to be quicker during exams. Thank you :)
By the way, the part where we use Pascals Triangle is coming from Leibniz Formula for those who want to understand why this works.
I have one question:
If d/dx(f(x,y)) = -fx/fy
It implies that df/dx is = 0 or not?
Because df/dx = fx + fy*dy/dx
(df/dx - fx)/fy = dy/dx
i love your chanel man , i wish i had seen this before my first calc 1 exam
I don't think the quotient rule should be taught as strongly as it is. Application of the chain rule and the power rule is a lot more instructive and less rote than applying a formula for quotients.
Really believe me the triangle was not invented by Pascal for the first time. He called Khyyam, a Persian Mathematician app 250 year before Pascal who invented the triangle as a coefficient in binominal expansion. Anyhow the triangle is called Khayyam-Pascal triangle to honor both.
nope it was formulated first in china stop lying
Thanks a lot!! You helped me to get prepared for my exam tomorrow!! You are awesome
Very glad to hear it! Best of luck.
Thank you from Egypt♥️
شكراً لك من مصر ♥️
You’re very welcome , have a great day!
well that looks like standard way of doing it with extra steps.Don't get me wrong ,these are nice tricks but knowing product rule and power rule with chain rule is very neat rather than knowing a hundred different rule
This deserves 1 million views thank you so much
You're very welcome, glad you enjoyed the video!
These are really useful but there are some problems I can't get the tricks to work with, like ones that would involve multiple tricks. Do these only apply if you can use one trick?
Ex: e^(y)cos(x)=1 + sin(xy)
Or perhaps I really just don't know what I'm doing. c: I'm tryin' though!
I think for this you need to get zero on one side then maybe the trick will work.
Thank you Brian, I always learn something when I watch your shows. Only one comment, if I may, try not to pronounce the T in the word often.
Excellent channel, thank you!
O my god...am gonna subscribe n its gonna be 200K ..oo I waited for this try many times...lalalalala
I developed all these myself practicing
well not all of them sorry i didnt saw the whole video, the second one a teacher told me for integration, third one was given in my book cengage a very renowned book here in india for jee prep
Excellent
y can use btc?
Please upload some more videos sir 🙏🙏🙏🙏🙏🙏🙏
The ad-bc in the 2nd trick looks suspiciously like the formula for the determinant of a 2x2 matrix, is this just coincidence or is there some link between the 2?
The formula is indeed basically like a determinant! There is certainly some connection!
Thanks 🙏
Thats just a application of the chain rule.
Will there be a minus sign in front of the answer in the 16:28 minute's example?
I'm confused, what were you writing on, and how were you writing backward.
How are you writing im so confused lmao ty for the vid tho
He is writing on glass simple is that
@@lordvenom4419 the question is if he's writing on glass then shouldn't it be flipped tho
@@Auoric sorry for making you wait 6 months, but the way he does it is that he writes normally to begin with and then he flips the video in editing
Thanks a lot!! sir I'm hoping to take masters in maths . like u.............)
You can do it! Best of luck!
Love it 😍
Great! Have a nice day.
3:20 DO I SEE A DETERMINANT?
Seriously though, is this pointing to some kind of connection with matrices?
Basically yes! Nice spot!
Not tricks! These are shortcuts at best, learned from years of use. Kind of how we can decompose equations into various forms to more readily extract information from them, and later extrapolate to a general form, like we do reducing the steps to get and then applying the quadratic formula to get the roots.
What will happen if I use the implicit trick on my AP Calc AB MCQ portion where they can't see the work?
I love you man 🤞
Pascals triangle
1
11
11^2
11^3
11^4
.
..
..
.
How can I thank u?
Memorizing is not the way to learn math. It is better to teach the principle of the math.
15:36
Awesome video
Thanks!
what is this hi-tech high technology?
or did the guy just wrote the inverted/mirrored form of the equations?
I think he’s just filming while standing behind a clear glass window. He writes normally with his right hand then just inverts the video to publish.
The root one wasnt a trick it is what sum1 would do
you look like nick jonas , btw , great content
@13
0-7
Derivatives is not that hard but integration sucks me a lot
You're right. Integration is usually much harder. Thanks for commenting!
Derivative of 1/x^2 is -2x
Nop
are you writing this backwards?
video editing :)
Sir i have a formula of that faster than yours😊
I’d love to know it!
@@BriTheMathGuy sir would you be my co author? lets present.i want it to be recognize.
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