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 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 so much for this video. I was looking all over RUclips 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.
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.
@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).
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!
@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.
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!
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.
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"
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..???
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?
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.
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?
@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.
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?
@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.
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??
Answer 4 years later... Or anyone who's still finding it confusing... Think of it as... You're taking out -1/2 power, thus what do you do to get back to equal the Original 1/2 power?? Well, Algebraically--->>> The Original Power of 1/2 MINUS WhatYouTakeOut. Thus, 1/2 - -1/2 becomes 1/2+1/2=2/2. 2/2 is 1 when simplified. Thus, 1 is the missing power you're looking for. Hope that helps.
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?
I fucking love you man
.....
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 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.
@rycecorl yea... the chain rule can be tricky at first! stick with it though - it will come to you
You save my life !!! My math assignment due tonight and I didn't know nothing! haha!!
Great stuff Patrick. Thank you for all the great instructional videos, you are easily THE best virtual tutor I've come across on RUclips. Cheers.
nice one uncle Patrick may God bless you
@707Cookiez no problem, happy to help: )
brilliant.. best instructional i've come across. Thanks Pat!
Good old quotient rule and good old Patrickjmt's videos
Thanks for putting these hard examples up! They're really helpful!
@MrCaRTom my pleasure!
I have Calc. exam tomorrow and you came to save my life!
Great job explaining the steps. You really helped me, Thanks!!!!
Impressive skills. Had to go back on a few parts to complete understand what you were doing but glad I watched this.
Just donated $5 ! Don't stop what you're doing, you've helped me so much!
Thank you! You do a really good job explaining what to do!
thank you so much for the good videos.
it makes the chain rule easier than the way my teacher explained.
Thank you so much for this video. I was looking all over RUclips 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!
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 :-)
This guy has won my heart.
dude, i just spend 2:30 hours watching your videos. crazy but honestly, you are driving me into math. thanks so much.
Oh my goodness, I missed my class when we learned the chain rule. You are my hero. :l Thank you!
You have just made me semi confident for my next exam, thanks for the videos!
@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.
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.
I can't believe how easy you make math, Patrick.
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.
@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).
9 years old and still useful, thanx from the UK.
Thank you! This was much needed!
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.
@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.
thanks sooo much for taking the time to make these video! I truly understand now
love your work. thanks heaps!
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 these video's are really well done, thanks
Thank you! I always freeze up when it comes to quotients and radicals, very tricky they are!
@Kn1ghtWing no problem : )
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!
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.
Thanks for making video please upload more video regarding this topic
Fractions are way less scary now. My hero!
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
definition of awesome: patrickJMT
your saving my ass dude big props i was just wondering do you basically cover all of grade 12 calculus?
@DeathG4n happy to help!
Why did I not find this sooner?
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..???
You guys think your teachers are bad, I'm teaching this to myself!
And I get it with this guy!
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?
@smarties1126 ok. so i am not crazy : )
Well done. Thanks!
So the 2x in the numerator is from using the chain rule a second time on the :
" 1/2(x^2+1)^(-1/2) "?
Beautiful!! This really is a big help!!
so much help. thanks a lot! you keep on inspiring me to become an engineer :D
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.
You are a Genius.. Thanks a lot for your amazing videos PatrickJMT..:D You are awesome..:)
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?
Thanks Patrick, I have found your video's really helpful. Big ups to you for your contribution to humanity ! :P
Awesome as usual
what i did not understand when you took out (x ) i mean from 4:05 to 4:29 please answer me man >>>>>>tnx
thanks dude! you gave me hope on passing my subject.. :D
If i cubed first the function then get the derivative using the quotient rule , can i still get the right answer. ?
So true!! The calculus is EASY. I just lost a lot of points on a test because of the algebra part.
@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.
@rainebf2 i do not see why it matters.
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?
Would I be able to use the rules of natural logs for this problem?
no problem!
Thank you. This is nice
Thank you soo much for this video
do you take the derivative of the 2x and multiply by 2?, i dont know when you stop taking derivaitve
Nice video, like any worthwhile subject, the chain rule takes practice.
Good job 👌
@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.
@Zestzima you can make a $5 donation now ;)
Awesome. Thank you so much!!!!
Thanks man, great help.. ps. my teacher doesn't allow radicals in the denominator.. but very informative!
So nice thanks sir
Why at 2:25 did you take the derivative of the already differentiated 1/2(x^2 +1)^-1/2 ?
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 are a godsend!
hi!!how would I solve f=(x/x+1)^3 using the chain rule
Have a doubt. Why did you put 2x at last in the second step?
I love you explanation but I am confused about the exponents factored (x^2+1)^-1/2 .plz help
Answer 4 years later... Or anyone who's still finding it confusing...
Think of it as... You're taking out -1/2 power, thus what do you do to get back to equal the Original 1/2 power?? Well, Algebraically--->>> The Original Power of 1/2 MINUS WhatYouTakeOut. Thus, 1/2 - -1/2 becomes 1/2+1/2=2/2. 2/2 is 1 when simplified. Thus, 1 is the missing power you're looking for. Hope that helps.
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.
Thank you so much!
Thank you, my dear man.
where did you get the 2x from at step 2?
Excelente colega
What happenwd to the exponent on the (x^2+1)^1/2 when u took out the (x^2+1)^-1/2?
how are you able to cancel out the 1/2 and 2x at 4:30?
sir, you took my stress away :]
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?
How did you get 2x at the end while doing the quotient rule of the inside?????
on the quotient rule, did you forgot to square the denominator ?
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)
I've got probably the worst calculus AB teacher in existence, thank you so much for clearing everything up for me dude
that part at 4:10 where you get the 2/2.. could you please explain that further??
PS thanks for keeping me from failing calculus :)