I really have to say, I've been in university for a little over two months now, and my math was going to be the death of me, but your videos have really helped. I really can't explain the relief of knowing that there is somewhere I can go to get a real human being to explain something to me rather then a 5 paragraph text book definition of what chain rule is and how to apply it.
Thank you for showing the algebra involved to simplify the problem after the calculus. A lot of videos don't show simplifying the problem to the final answer, and we don't go over any of that in class since we've technically already learned it, but it's a nice refresher.
Im a Junior in college and I wanted to review derivatives just for the hell of it, and I realized idk how I would have gotten through calculus without JMT. You da man!
Thank you so much for this video. I was looking all over UA-cam trying to find a video that used the chain rule like you just did. I needed a refresher for factoring out negative and fractional exponents. I wish I found this sooner because I've been stuck on the same type of problems for days. Thank you!!!
@MIT2004 no, i did take precal in high school, but i was a pretty terrible student at that point, so i retook precal in college. my algebra has always been solid, but the trig i did not get until college.
@patrickJMT My Calculus BC teacher also said that it makes it easier to divide by hand. He doesn't require rationalizing the denominator because it is just a remnant from the days when we didn't have calculators.
Thanks very much for not keeping your knowledge but always sharing. The greatest gift men can give is to share their knowledge with the rest of the world.
Patrick! Your amazing man! Most teachers think they can teach just because they have a degree in math. NO! No one cares about your background in math if you can't explain it to your students. Thanks patrick. I certainly do appreciate your videos!
@patrickJMT other than it puts things in a standard form and makes some division by hand easier. there is no mathematical reason why it must be done though. ask your teacher and see what they say (i'm not sure, will most likely be the answer).
@rainebf2 i'd give you full credit. just depends on the instructor. i have never been given a good reason as to why one needs to rationalize the denominator.
@Gooldude3 : when finding the derivative of the inner function with the chain rule,, you square the denominator and since the original denominator was raised to a 1/2 power, squaring that would mean multiplying those powers, and 1/2 times 2 leaves the denominator raised to the power of 1. Thats why it looks that way.
Wow. My teacher would try to explain this and I would be fine up until he would start factoring out. At that point I just get LOST. But everything You said made sense. Thank You sir.
i'm a 2nd year university student struggling with calculus. i'm sure most people watching these videos are just like me and have no means of buying a mercedes... so why are they putting ads here.
@patrickJMT yeah, so I asked, pretty much here in Australia "most simplified form" means that we have to rationalize the denominator for our final answer. So if the question on an exam was worth let's say 6 marks, and you wrote as your answer 1/root2 instead of root2/2, you'd only get 5/6 marks. That's just the way the state marks so the teachers drill into us to rationalize or otherwise we'll lose dumb marks :/.
think of factoring like dividing and you want to divide the common factor with the smallest exponent from each term.....so since -1/2 is smaller than 1/2, you divide out the (x^2+1)^-1/2.....so, when you divide (x^2+1)^1/2 by (x^2+1)^-1/2 you just subtract the exponents: 1/2-(-1/2) = 1/2+1/2 = 1....so that's why you're just left with x^2+1.... hope that made sense! =)
Thanks for making all these videos! They've really been helping me a lot in my calculus class! I have one question i was wondering if you could help me with though! " use the product rule and the chain rule to prove the quotient rule"
ok so for that part he is trying to find g' when g is (x^2+1)^1/2, and to differentiate this you use the (i think chain rule) so do this you bring the power to the front, the 1/2, multiply this by what's in the the brackets but put it to the same power as before -1 so (x^2+1)^-1/2 and then you differentiate what's inside the brackets which becomes 2x and multiply the three things together so it is 1/2(x^2 + 1)^-1/2(2x) which is what the guy got as well, I hope i explained this well enough
When he factor out the numerator, where do all the terms go. I don't see how they cancelled and I'm sure it's right in front of my face. How are we only left with ONE (x^2+1)^1/2 term when factoring. Shouldn't there be a 1 left on the inside to multiply by..???
just wondering..instead of factoring out the [(x^2+1)^-1/2], why cant you bring it down to the denominator, make the exponent positive and cancel it with the exact terms that are in the numerator?
So I understand everything about how chain rule works, but I just don't understand WHEN you shoukd use it. Is it used any time you are taking the derivative of something that has an exponent other than 1, since then it's basically like an outside-inside function?
@yodellikeyoumeanit09 when u multiply x^-1 and x^2 you get x^1....you add powers.. so he essentially multiplied x^-1/2 and x^1 ... 1- 1/2= 1/2 which is what was originally given. I am sure in Calculus 1 or beginning calc you can get by without simplifying so much but hey, if its possible do it.
He took that exponent in denominator so it was: (x^2+1).(x^2+1).(x^2+1)^1/2.. add powers of first two term i.e (x^2+1).(x^2+1) = {(x^2+1)^2} Now we have {(x^2+1)^2}.(x^2+1)^1/2. Now similarly add powers to get:(x^2+1)^5/2 Regards Karan Dhillon :)
@con5tant because 1/2 times 2X is X as its pretty much half times two which becomes one leaving the X, try it on your calculator or something 0.5 times 2 = 1
THIS CHAIN RULE IS SOME GODDAMN MIND BLOWING METHOD. IT DOES NOT MAKES ANY SENSE SO IT REALLY IRRITATES ME BUT I'LL TELL YOU WHAT: I WONT GİVE UP UNTIL I GOT THIS THING IN MY POCKET. STAY HARD AND WORK WITH YOUR ANGER, HUNGER AND AMBITION TO PROSPER. EITHER DO THIS OR KNEEL LIKE A COWARD CHICKEN.
Hello!, I am taking a Calc 2 class this upcoming fall. I took a Calc 1 class a couple years ago and haven't practiced much with math since. Does anyone have any study suggestions on material I should focus on before the class starts to freshen up on?
@patrickJMT in terms of an exam response / test response, i know that in our class at least (year 12 maths) we'd lose a mark for not rationalizing the answer.
In ur final answer could u simplify the square root and the power five and get the eqaution ^3? Does that work or is that illegal? Does that make sense?
when you multiply the two fractions with each other why do you multiply their bottoms as well? for example when you multiply 3/2 and 4/2 wouldn't you normally have gotten 12/2 instead of 12/4??
Im so confused... After using the chain rule the first time we still end up with a square root in our answer. Doesn't that mean we must use the chain rule again (eg. multiply by the derivative of the radicand)?
+John Parks There isn't anything wrong with having a radical in our answer here. After we've undergone all the steps he's illustrated in the video, we're done finding the derivative, and there's nothing left to do
I really have to say, I've been in university for a little over two months now, and my math was going to be the death of me, but your videos have really helped. I really can't explain the relief of knowing that there is somewhere I can go to get a real human being to explain something to me rather then a 5 paragraph text book definition of what chain rule is and how to apply it.
Thank you for showing the algebra involved to simplify the problem after the calculus. A lot of videos don't show simplifying the problem to the final answer, and we don't go over any of that in class since we've technically already learned it, but it's a nice refresher.
I fucking love you man
.....
dude, i just spend 2:30 hours watching your videos. crazy but honestly, you are driving me into math. thanks so much.
You save my life !!! My math assignment due tonight and I didn't know nothing! haha!!
Just donated $5 ! Don't stop what you're doing, you've helped me so much!
I have Calc. exam tomorrow and you came to save my life!
Im a Junior in college and I wanted to review derivatives just for the hell of it, and I realized idk how I would have gotten through calculus without JMT. You da man!
Oh yeah, he saved my ass, too - 6 years ago.
Thank you so much for this video. I was looking all over UA-cam trying to find a video that used the chain rule like you just did. I needed a refresher for factoring out negative and fractional exponents. I wish I found this sooner because I've been stuck on the same type of problems for days. Thank you!!!
come back any time!
@MIT2004 no, i did take precal in high school, but i was a pretty terrible student at that point, so i retook precal in college. my algebra has always been solid, but the trig i did not get until college.
@707Cookiez no problem, happy to help: )
@patrickJMT My Calculus BC teacher also said that it makes it easier to divide by hand. He doesn't require rationalizing the denominator because it is just a remnant from the days when we didn't have calculators.
nice one uncle Patrick may God bless you
Thanks very much for not keeping your knowledge but always sharing. The greatest gift men can give is to share their knowledge with the rest of the world.
Patrick! Your amazing man! Most teachers think they can teach just because they have a degree in math. NO! No one cares about your background in math if you can't explain it to your students. Thanks patrick. I certainly do appreciate your videos!
Wow that was such a great video. Even my teachers couldnt have made this any easier. :D
Perfect!
+patrickJMT People like you are making schools redundant. True hero.
@MrCaRTom my pleasure!
@patrickJMT other than it puts things in a standard form and makes some division by hand easier. there is no mathematical reason why it must be done though. ask your teacher and see what they say (i'm not sure, will most likely be the answer).
You guys think your teachers are bad, I'm teaching this to myself!
And I get it with this guy!
Great stuff Patrick. Thank you for all the great instructional videos, you are easily THE best virtual tutor I've come across on UA-cam. Cheers.
brilliant.. best instructional i've come across. Thanks Pat!
Good old quotient rule and good old Patrickjmt's videos
@Kn1ghtWing no problem : )
This guy has won my heart.
I can't believe how easy you make math, Patrick.
@rainebf2 i'd give you full credit. just depends on the instructor. i have never been given a good reason as to why one needs to rationalize the denominator.
9 years old and still useful, thanx from the UK.
@DeathG4n happy to help!
@Gooldude3 : when finding the derivative of the inner function with the chain rule,, you square the denominator and since the original denominator was raised to a 1/2 power, squaring that would mean multiplying those powers, and 1/2 times 2 leaves the denominator raised to the power of 1. Thats why it looks that way.
Impressive skills. Had to go back on a few parts to complete understand what you were doing but glad I watched this.
WOW, I'm so glad I came across your videos. Thanks so much, you saved the $35 an hour I would pay for a tutor!
@rycecorl yea... the chain rule can be tricky at first! stick with it though - it will come to you
Wow. My teacher would try to explain this and I would be fine up until he would start factoring out. At that point I just get LOST. But everything You said made sense. Thank You sir.
i'm a 2nd year university student struggling with calculus. i'm sure most people watching these videos are just like me and have no means of buying a mercedes... so why are they putting ads here.
i'm in grade 12 lol definitely not buying a mercedes anytime soon...
the google ad's algorithm is shitty
whitehawk38 Why aren't you using adblock
So patric gets paid for his hard work! he deserves every single penny and more.
I'm 2nd year grad student and the mercedes ad has persuaded me on my next motor vehicle purchase. Leaving for dealership soon.
they are being multiplied. you can pull multipliers to the front and combine like terms which ends up being 2/2 or 1.
I've got probably the worst calculus AB teacher in existence, thank you so much for clearing everything up for me dude
thank you so much for the good videos.
it makes the chain rule easier than the way my teacher explained.
Oh my goodness, I missed my class when we learned the chain rule. You are my hero. :l Thank you!
You are a godsend!
You have just made me semi confident for my next exam, thanks for the videos!
Thanks for putting these hard examples up! They're really helpful!
thanks sooo much for taking the time to make these video! I truly understand now
no problem!
Your videos have REALLY helped me understand derivatives sooo much better! Thanks a million! Now, hopefully I won't space out on my exam today :-)
@patrickJMT yeah, so I asked, pretty much here in Australia "most simplified form" means that we have to rationalize the denominator for our final answer. So if the question on an exam was worth let's say 6 marks, and you wrote as your answer 1/root2 instead of root2/2, you'd only get 5/6 marks. That's just the way the state marks so the teachers drill into us to rationalize or otherwise we'll lose dumb marks :/.
think of factoring like dividing and you want to divide the common factor with the smallest exponent from each term.....so since -1/2 is smaller than 1/2, you divide out the (x^2+1)^-1/2.....so, when you divide (x^2+1)^1/2 by (x^2+1)^-1/2 you just subtract the exponents: 1/2-(-1/2) = 1/2+1/2 = 1....so that's why you're just left with x^2+1....
hope that made sense! =)
Thanks for making all these videos! They've really been helping me a lot in my calculus class! I have one question i was wondering if you could help me with though!
" use the product rule and the chain rule to prove the quotient rule"
@ItsJad ha, glad my stuff makes sense for you
ok so for that part he is trying to find g' when g is (x^2+1)^1/2, and to differentiate this you use the (i think chain rule) so do this you bring the power to the front, the 1/2, multiply this by what's in the the brackets but put it to the same power as before -1 so (x^2+1)^-1/2 and then you differentiate what's inside the brackets which becomes 2x and multiply the three things together so it is 1/2(x^2 + 1)^-1/2(2x) which is what the guy got as well, I hope i explained this well enough
Fractions are way less scary now. My hero!
definition of awesome: patrickJMT
your saving my ass dude big props i was just wondering do you basically cover all of grade 12 calculus?
So true!! The calculus is EASY. I just lost a lot of points on a test because of the algebra part.
How did you get 2x in the quotient rule if the formula for the numerator states:
g (x) f`(x)-f (x)g`(x)
And you wrote:
g (x) f`(x)-f(x)g'(x) g''(x)
Never mind I understand, in order to take the derivative of g(x) you must use the chain rule
Thank you! I always freeze up when it comes to quotients and radicals, very tricky they are!
When he factor out the numerator, where do all the terms go. I don't see how they cancelled and I'm sure it's right in front of my face. How are we only left with ONE (x^2+1)^1/2 term when factoring. Shouldn't there be a 1 left on the inside to multiply by..???
Why did you bring (x^2 + 1)^-1/2 down to the denominator (4:53)? I didn't know you could do that.
Actually...I can see why. I would have never thought of that step on my own though.
just wondering..instead of factoring out the [(x^2+1)^-1/2], why cant you bring it down to the denominator, make the exponent positive and cancel it with the exact terms that are in the numerator?
Nice video, like any worthwhile subject, the chain rule takes practice.
4:54 how come do you pull (x^2+1)^-1/2 down? EDIT: NVM, got it (it's ^-1/2, so by removing the - we move the whole piece to the denominator)
@1:48 Patrick takes the denominator up in the numerator but leaves 1/2 in the exponent. Should it not have been ^-1/2?
Thank you soo much for this video
i love u man.....hw+studing=5minutes
Writing the function with 1/2 on the outside is the equivalence of the square root of the function. They're both the same.
Wow these video's are really well done, thanks
Why at 2:25 did you take the derivative of the already differentiated 1/2(x^2 +1)^-1/2 ?
on the quotient rule, did you forgot to square the denominator ?
So I understand everything about how chain rule works, but I just don't understand WHEN you shoukd use it. Is it used any time you are taking the derivative of something that has an exponent other than 1, since then it's basically like an outside-inside function?
i think an easier way to think about it, is: x³′ = 3x²*1 , the 1 is x` so that you won't forget the inner part in more complicated derivatives..
Thanks Patrick, I have found your video's really helpful. Big ups to you for your contribution to humanity ! :P
You are a Genius.. Thanks a lot for your amazing videos PatrickJMT..:D You are awesome..:)
@rainebf2 i do not see why it matters.
@yodellikeyoumeanit09 when u multiply x^-1 and x^2 you get x^1....you add powers.. so he essentially multiplied x^-1/2 and x^1 ... 1- 1/2= 1/2 which is what was originally given. I am sure in Calculus 1 or beginning calc you can get by without simplifying so much but hey, if its possible do it.
Would I be able to use the rules of natural logs for this problem?
He took that exponent in denominator so
it was: (x^2+1).(x^2+1).(x^2+1)^1/2..
add powers of first two term i.e (x^2+1).(x^2+1) = {(x^2+1)^2}
Now we have {(x^2+1)^2}.(x^2+1)^1/2.
Now similarly add powers
to get:(x^2+1)^5/2
Regards
Karan Dhillon :)
Thank you! You do a really good job explaining what to do!
@con5tant because 1/2 times 2X is X as its pretty much half times two which becomes one leaving the X, try it on your calculator or something 0.5 times 2 = 1
so much help. thanks a lot! you keep on inspiring me to become an engineer :D
what i did not understand when you took out (x ) i mean from 4:05 to 4:29 please answer me man >>>>>>tnx
THIS CHAIN RULE IS SOME GODDAMN MIND BLOWING METHOD. IT DOES NOT MAKES ANY SENSE SO IT REALLY IRRITATES ME BUT I'LL TELL YOU WHAT: I WONT GİVE UP UNTIL I GOT THIS THING IN MY POCKET. STAY HARD AND WORK WITH YOUR ANGER, HUNGER AND AMBITION TO PROSPER. EITHER DO THIS OR KNEEL LIKE A COWARD CHICKEN.
Thanks man, great help.. ps. my teacher doesn't allow radicals in the denominator.. but very informative!
Can you use the outside inside rule for all chain rules? because my teacher showed us this this rule and U-sub. and I prefer the outside inside rule.
Hello!, I am taking a Calc 2 class this upcoming fall. I took a Calc 1 class a couple years ago and haven't practiced much with math since. Does anyone have any study suggestions on material I should focus on before the class starts to freshen up on?
4:25 if you added the exponents... wouldn't it be zero...? Or does the negative sign flip or something.
+Jamison Drapeau -1/2 and +1/2 cancel each other and we are left with (x^2+1)
It's (2/1)*(1/2)
@patrickJMT in terms of an exam response / test response, i know that in our class at least (year 12 maths) we'd lose a mark for not rationalizing the answer.
Great job explaining the steps. You really helped me, Thanks!!!!
Why did I not find this sooner?
@Zestzima you can make a $5 donation now ;)
In ur final answer could u simplify the square root and the power five and get the eqaution ^3? Does that work or is that illegal? Does that make sense?
To make this easier you can use the natural log properties
How did you get 2x at the end while doing the quotient rule of the inside?????
Thanks for making video please upload more video regarding this topic
Thank you! This was much needed!
when you multiply the two fractions with each other why do you multiply their bottoms as well? for example when you multiply 3/2 and 4/2 wouldn't you normally have gotten 12/2 instead of 12/4??
you have a surd in the denominator, shouldn't you rationalize the denominator for your final answer?
thanks dude! you gave me hope on passing my subject.. :D
Hi Patrick! Great video, thanks for sharing! I'd like to point out a smile mistake however...@ 2:30 (0.5^2 is not = 1 it's 0.25).
Im so confused... After using the chain rule the first time we still end up with a square root in our answer. Doesn't that mean we must use the chain rule again (eg. multiply by the derivative of the radicand)?
+John Parks There isn't anything wrong with having a radical in our answer here. After we've undergone all the steps he's illustrated in the video, we're done finding the derivative, and there's nothing left to do
I see. I always have trouble figuring out when to stop using the chain rule! Thank you for your help though!
Have a doubt. Why did you put 2x at last in the second step?
Beautiful!! This really is a big help!!
6:17 ummm, wasn't the square root supposed to be removed from the denominator? I thought that there should be no square roots in the denominator?