Chain rule for derivatives, with product rule (KristaKingMath)
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- čas přidán 2. 08. 2024
- ► My Derivatives course: www.kristakingmath.com/deriva...
Learn how to use the chain rule to calculate the derivative of the product of two functions. To use chain rule, you'll need to identify an inside and outside function. When you take the derivative of the function in general, you'll take the derivative of the outside function first, leaving the inside function completely untouched, then you'll multiply your result by the derivative of the inside function.
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If you could use some extra help with your math class, then check out Krista’s website // www.kristakingmath.com
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Hi, I’m Krista! I make math courses to keep you from banging your head against the wall. ;)
Math class was always so frustrating for me. I’d go to a class, spend hours on homework, and three days later have an “Ah-ha!” moment about how the problems worked that could have slashed my homework time in half. I’d think, “WHY didn’t my teacher just tell me this in the first place?!”
So I started tutoring to keep other people out of the same aggravating, time-sucking cycle. Since then, I’ve recorded tons of videos and written out cheat-sheet style notes and formula sheets to help every math student-from basic middle school classes to advanced college calculus-figure out what’s going on, understand the important concepts, and pass their classes, once and for all. Interested in getting help? Learn more here: www.kristakingmath.com
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Too pro. I love people like you who take the time to make these videos. The payoff for humanity is huge. Thank you fellow human being
Your videos have been a huge help! Back in '06 I failed precalculus after my third attempt and switched to liberal arts- but now I'm studying financial economics and getting A's on my calculus tests!!!
honestly....this is better than khan's video on this topic...Bravo krista, great effort dear, keep it up!!☺
Thanks! I'm glad you liked it!
That's right Ali.
I never miss a chance to say "Krista is the best teacher on CZcams", one reason being that if all the other CZcams teachers copy her methods Exactly, the world's GDP will rise.
I have watched and read several articles on this rule and your presentation is the only one that makes sense. Thank you!!
The run through with the simplifying was the best I could find on CZcams! Thank you so much! :))))))))))))
I can't believe you positively responded to almost every comment. You are like the most attentive tutor on the whole net!! But it must be nice to know you provide such a helpful service. Thanks bunches.
You are so welcome! Thanks for the comment. :)
This video was amazing and so clear! Thank you for doing these videos and I hope to see more, please don't stop! Your concept is the best so far that I have seen. Can't wait to keep learning from you (:
Thanks for the kind words! I really appreciate it. :)
When I'm feeling down I just come here to listen to Krista's voice. I hate math and Krista makes it seem like I'm listening to the most amazing stuff on earth.
I really appreciate the comments! So I do my best to respond. :D
Thank you once again, Krista, for teaching such an important concept to us in your own wonderful way, as always.
Helped me understand this concept perfectly! Thank you for explaining so well!!
This was the exact question I got for homework. Bless!
lol
I'll continue to make more, but you can find the others here. :)
youtube . com/course?list=EC1CDF4BF496C30885
Krista, your videos have helped me tremendously in learning calc. You have a gift for teaching the abstract in simple clear language.
Thank you! I'm so glad to know that the videos have been helping! :D
Where, oh, where were you when I needed a math teacher in high school? Not that I'm having better luck in University...Stupendous! I've learnt more in a few hours of CZcams videos than I did in 4-6 months doing differentiation in high school.
This Is AMAZING !!! I'm an Engineer and i'm really so needy for the calculus as i started a course which totally depending on calculus and i couldn't remember it ! it's something since 6 years , so now i feel really i got it back to my brain ! thank you very much and everyone who's helping others ! Keep Going (Y) !
This is a really good problem. more complex and usign multiple rules. Much appreciated.
WOW good for you, that's awesome!! I'm so glad it made sense and was clear enough for you to understand it so quickly!! :D
Crystal clear explanation! Thank you so much!
Glad you liked it! :)
Great video if have just started the chain rule application!
I just found this channel today and it makes calculus seem too easy! Great teacher!
+Very Merry Dingleberry Thank you so much, I'm glad it's helping!
Thank you so much for this video! I kept getting stuck on this type of problem but finally realized my issue is that I was not factoring! Such a big help, I'm saving this video. Please keep them coming!
+Jason Moses I'm so glad it helped!
Your videos are absolutely the best. I had a gap between Calc 1 and Calc 2 and this has been a lifesaver as a refresher.
I'm so glad I could help!
THANK YOU THANK YOU THANK YOU!!! You took the time to explain this and I have been struggling so bad with this! I am so grateful to you!
You are so welcome, Denise! I'm so glad it all made sense! :D
This greatly improved my understanding of the chain rule. THANKS!!!
In my current Calculus class this was the most demanding part so far. Mainly because it requires a lot of multitasking. You have definitely cleared of up though with your video. Thank you so much!
David Alderman You're welcome, I'm so glad this helped!
Finally someone took a moment to explain this stuff, not just blindly solve it. Qute as well:)
Thank you so much! this video is most helpfull! Espetially for someone who skipped as many lectures as I did:)
Dear Krista (Calculus Expert) I truly cannot thank you enough for your EXCELLENT abilities with helping me with the "Chain Rule for Derivatives, With Product Rule. Unlike many of the on line (and college Calculus professors) YOU leave them far back at the "starting line." Krista your piece-by-piece explanation is absolutely superior. Thank you ever so much!!!! You have no idea how much you have helped me. I am not a student, however, I just have a love for mathematics (am disabled with severely painful spinal disease) . I started Algebra I and later completed Algebra II and enjoyed them so much. Your great knowledge and teaching abilities are just fantastic!!
+charlesrlassiter Thank you so much, Charles! I'm so glad I'm able to help, and that you're enjoying the videos! Keep your passion for math and keep learning. :D
That makes me so happy! I'm so glad this helped!! Good luck on your exam!! :D
I've been stuck on this problem for almost 4 hours!! THANK YOU SOOOOO MUCH! Life saver!! :)
Yay! So glad I could help. :)
I understood how to use the product rule, but I found myself stuck at the point where you have pull out a factor and simplify... I had no idea you could do that! This video has helped me a lot... thanks heaps and keep up the awesome work.
Thanks heaps. I learnt more in 9 minutes than I did in an hour long tutorial. You are a natural at this.
Thanks! I'm so glad I can help.
Very well explained. Again a million thanks!
This is the first time i've ever commented on a youtube video. I was struggling with a very similar problem for 2 days. This video cleared everything up in less then ten minutes. Thank you so much for what you do.
You're very welcome, I'm so glad it helped!!
always so helpful, thank you now I'm ready for my calculus test
that was very helpful i had a problem factoring out when it came to the third step ^^. now, it is clear for me, thank u! ^^
you just explained my professor's 2 hour lecture within 9 mins - I FREAKING LOVE YOUH!
Thanks for the help! Your video has helped me getting through my homework.
Thank you so much, this video was the best I've seen on these types of derivatives !!
Aw thanks! I'm glad you liked it. :)
You're always so supporting! Thanks! :)
I'm really loving your videos. I took Calculus 1 last year, and now I need to brush up to get ready for Calc 2. After searching through TONS of stuff on the internet, your videos continue to be the easiest to understand. I really appreciate all the time you must have invested into this. :D
Aw, thanks for giving me a big smile! :D I'm so glad they're helping!
THANK U SO MUCH FOR THIS DETAILED EXAMPLE! u are so articulate and u went thru the example in a very systematic organized manner tht was so easy to understand! i wish u were my prof lool!!
omg! have to report tomorrow and i began to cram where to look for help, i browsed, and browsed...i almost gave up but then i saw this! AMAZING! THANKS!!! You are a gift from Above ^^ Godbless!
+violet_butterfly I'm so glad you found the videos and that they're helping! I hope your report went well today!
i agree with everyone ... you're an amazing youtube teacher ! i actually learn and understand more from you than my teacher :p i didnt understand the chain and product rule together BUT you've reeeally helped me a lot ! keeeeep teaching and never stop (:
I'm so glad you found it!! Hope it's helping!! :D
I love how you explain everything so clear. What you do in a couple minutes my professor takes over 1hour and still NOT clear..
Oh my gosh, you just explained it beautifully! I think of all the videos that I have watched,, you have explained it the absolute best. And you don't speak fast, so I could undersitand you perfectly, When I was doing homework, I kept getting confused, and I don't think that will be an issue. Thank you!
You're welcome, Kristy! I'm so glad it made sense! :D
Thank you for the help. I don't know why I've never thought of factoring entire expressions before, but making that click will help me a lot in the future, I'm sure.
Oh good! I'm glad it helped! :D
Thanks, very well explained and easy to understand. Very much appreciated!
You're welcome! I'm so glad it helped!
I try and explain the process here :) integralcalc . com/how-I-create-my-videos/
I'm so glad they're helpful!! Thanks for saying hi!! :)
Forbidden fruit is always the best! Have been bunking school to watch these videos! My 12'th grade maths exam (Before undergraduate studies, in India) starts on the 18'th of March. Thanks!
Thank you so much! These videos are very helpful and concise!
Thanks Sara! I'm so glad they're helping. :)
Wow!! Amazing how easy you explained it. My professor is really good at explaining terms, but your method is much better. If I could like this tutorial and other that you made more than once I would.
Awesome! So glad I could help. :)
Math on a soft voice, that’s a first. Thank you very much Kris, it was very helpfull
AH! TY TY! I have Mid year exam tmr, I understood everything but had this jumbled in my head. I always did one rule but not the other, you made it so clear to me! Ur awesome!
Once again, thank you so much.
Your videos are a big help, and because of you I feel confident that I will do well in Calculus.
I'm honored! And I hope you do GREAT in calculus!!
i'm so glad it helped!! good luck on your test! :D
you are just FABULOUS!
bring the test!!!!!!!
Yay! I'm so glad I could help refresh your memory! :D
You have no idea how much your videos help me! I most certainly Praise Father God for the blessing that you are! And i thank you for having a generous and empathetic heart!
Thank you so much, I'm honored to be able to help!
Great!!! Better explanation than my teacher! Keep up the good work!!! Thanks!!
Thank you very much!, I will be watching more of your videos in the future
You're welcome!
Finally...someone who can speak to normal people!!! I am normally the person who just gets things with all types of mathematics...for whatever reason, this chain rule thing threw me for a loop and I have been lost for over 2 weeks now. Well, you saved me with this video! Thank you so much!!!!!
Thanks so much!!! Very helpful and you did a great job!
Aw thanks!
u r a life saver , thank u so much for the videos , it helps a lot
if you need help solving that exact problem, try plugging it in to wolframalpha . com! it should give you the step-by-step solution and the answer. :)
Your videos are realllly helping me with my calc class!
Yay! :D
Thanks!
Glad I could help! :)
I watched this yesterday, didn't make sense. Watched this today, made sense! Thanks for the video, cleared things up!!!
+MusicLyrics101 I'm so glad it helped!
+CalculusExpert.com how about finding the derivative of the function
y=10 ^ (1-x^2)
Your video is so clear and helpful!
I'm glad it helped!
thanks a lot, i am sure many people will appreciate this video. from now on i am a follower to this channel.
Awesome, thanks! :)
Got confused to factorize. watched it twice, eventually helped me.. thanks
I love you! I had so much trouble with this! Thank you
You're welcome, Tim! I'm so glad it helped to clear things up! :)
Great tutorial, thanks!
Just started chain rule in class on Monday night and I was completely lost. I mean, DEEPLY concerningly lost! lol
I watched the prior video and now this video, and it makes COMPLETE sense now!!! The idea that its power rule that leads into chain rule was so helpful. That literally was the "ah HA!!" moment for me.
Thank you and FIY, I purchased Calc 1. I know it will help! Thanks Krista!!
Thank you so much Brian! I'm so glad this helped... chain rule is not easy.
Thanks a lot! Really helped me for my Calc test preparation.
You're welcome! Good luck on your test!
You are like a goddess from above!! Thanks for saving my hw!!!! You rock!
I'm so glad it helped!
This video is so helpful. Thanks to you!
Glad it could help! :)
I love your videos. You helped me so much THANK YOU
OMG GOD bless you
Very helpful video. Thanks a bunch!
Thanks for letting me know!
awesome! thanks pretty lady for explaining it so easily
you're welcome! i'm so glad the video made sense, and i'd be happy to be your professor on youtube!! :D
you're welcome! i'm so glad it helped!! :D
That makes me happy! Thanks for letting me know! :)
Thank you so much!! This video really helped me with my math homework!
:D
Thanks for the comment. :)
Integral Calc, This is brilliant!!
You are simplifying many peoples lives and indeed changing the world in your own special way. Naphtal
Aw thanks! I'm just glad I can help. :)
Thank you very much!
And praises for the videos I've seen so far! You're doing great! :-)
Thank you very much for this wonderful video! You make Calculus easy to understand, and you're one of the reasons I scored a 103 and 95 on my first two exams :)
That's so awesome! You still had to put in the all of the work. But I'm glad I could help. :)
My teacher is really confusing and talks over my head I'm in class. Help comes from unexpected places sometimes. Thank you so much and keep the videos coming!
Thank you!! this really helped with my calculus HW.
+Haru Saeng You're welcome, I'm so glad it helped!
Hot and smart! Thank you! You have a video for basically every problem I run into.
You're so welcome! :)
THANK YOU! That was an excellent explanation, not to mention, you're a trooper for powering though all the algebraic simplification with such gracefulness. haha
:D