❖ The Product Rule for Derivatives ❖

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  • Опубліковано 1 лют 2025

КОМЕНТАРІ • 375

  • @karzmaniac
    @karzmaniac 12 років тому +4

    i love how this guy is such a gentleman. always apologizing if he moves the paper slightly and saying "excuse me" after he coughs a little. just makes this much more enjoyable to learn from. bravo sir bravo.

  • @ajeje1996
    @ajeje1996 8 років тому +6

    In highschool I went to a classical lyceum and I studied a lot of latin and ancient greek, and basically no math for five years. In a month I'll take an admission exam which requires general knowledge of derivatives, and these videos are helping me a lot, thank you so much!

  • @WVerkaart
    @WVerkaart 12 років тому

    Patrick,
    I am from The Netherlands. I am 48 years old and since 1 year a math teacher.
    Since I became a teacher at my age I look a different way to your video''s.
    I want to say to you, you are are real artist.
    Just a piece of paper and a pen, with the right words, the good chosen examples.
    And you make people understand it.
    I use your video''s often.
    Thank you for your piece of art.
    br
    Walter

  • @patrickjmt
    @patrickjmt  16 років тому +1

    in your case, I would just multiply it out.
    In general, suppose that
    p(x) = f(x)g(x)h(x), then
    p'(x) = [f(x)g(x)]'h(x) + [f(x)g(x)]h'(x)
    so that you will have to do the product rule 'within' the product rule, on the f(x)g(x) factor. Basically group two of the three together and use product rule from there!
    hope this makes sense!!

  • @HeysaysChenay
    @HeysaysChenay 12 років тому

    Patrick you are amazing, I've been watching your videos since Precalc 126, then again in 127, and now I'm in my last math class ever, 181! I'd like to attribute my success to you!

  • @akro286
    @akro286 11 років тому +1

    Man, You are really amazing! I've taken all this at my uni but then i was just walking on water with what i knew.. now I'm on solid ground, ALL thanks to you!

  • @rynoweston
    @rynoweston 11 років тому

    Thanks for this. My teacher is from India and I couldn't understand this when she was explaining it. You're the man. This is so much more helpful than tutoring.

  • @ler1964
    @ler1964 8 років тому

    Your videos are making these summer classes so much easier. I really appreciate the time you take out of each video to properly explain the topic so we can understand it properly. Keep up the good work.

  • @nellycorture
    @nellycorture 13 років тому

    i love your vids! I waste sooo much time in calculus class, learning absolutely nothing, then i come home and watch one 8 minute video and understand it completely!

  • @BekaEthio
    @BekaEthio 9 років тому +7

    I don't read the text book and I don't go to the class room but I scored 95/100 ONLY USING UR VIDEOS.Thank you!!!
    The order of the videos doesn't looks OK to me for this chapter(Derivatives) video ~15 to ~25.

  • @1997milesaway
    @1997milesaway 9 років тому +33

    Thank you very much, this helped me a lot! I was trying to understand it by reading the textbook but idk wtf they were doing lol

    • @patrickjmt
      @patrickjmt  9 років тому +23

      Come back any time , I have a ton of calc videos, at least one for just about every topic you see in calc

  • @jadsalloum684
    @jadsalloum684 11 років тому

    Hey Patrick! Just wanted to tell you that me and the guys here at the American University of Beirut thank you a lot for helping us get past these math classes and into our domain! Much thanks from Beirut, Lebanon.

  • @abdullahiahmed2435
    @abdullahiahmed2435 6 років тому

    My intention for coming to this video was to watch it fully but guess what .....the formula made me fully understand what I was struggling at. Thank you, sir!!!

  • @jrp7808
    @jrp7808 14 років тому

    In the past hour I have learned the quotient rule, chain rule, and the product rule. Whereas before I had no clue how to do any of them. Brilliant!

  • @monicasocal
    @monicasocal 11 років тому +117

    Your voice is so encouraging…… I can do it!

    • @patrickjmt
      @patrickjmt  10 років тому +33

      yes, yes you can.
      one's attitude is a good part of being successful in math (as in most challenging things in life).

    • @DESTER10984
      @DESTER10984 10 років тому +1

      patrickJMT Patrick can you tell me how to one that is much bigger I can do it if I follow what you showed on this video but it turns out to be too big for such a simple product. The problem is
      f(x)=(x^3-2x+1)^4 that exponent of 4 makes it incredibly huge

    • @davidg5189
      @davidg5189 10 років тому +4

      Dexter8x that problem you should just use chain rule
      (3x^2-2).4(x^3-2x+1)^3

    • @birhanu13
      @birhanu13 10 років тому

      Dexter8x o

    • @simundo555
      @simundo555 9 років тому +1

      +Dexter8x
      correct you can use the chain rule.

  • @quat56
    @quat56 14 років тому

    thanks Mr Patrick all your Free Math Tutorial Videos are Red-hot gem ,I'm currently pursuing my Masters Degree Course i.e (M.A in Economics) at my Hometown University.. Since I didn't have an Advance Math Background in Economics during my Undergraduate College level ..I find it extremely difficult to understand the catch 22 ways in which a typical Math Textbook explains these concepts without explaining their Logical Rationale ..Your Explanations of Calculus & Derivatives r so Clear & Sunny.:D

  • @patrickjmt
    @patrickjmt  16 років тому

    i am happy u think so! i got most calc 1 and 2 here, so come visit any time!!

  • @patrickjmt
    @patrickjmt  14 років тому

    @Seedofwinter well, it is just 'one function ' but to get it, you have to multiply two other functions! if there is any multiplication that occurs within the function, you have to use the product rule.

  • @Wpayne8
    @Wpayne8 12 років тому

    I love you Patrick! This is my 3rd calculus course and you're still my go-to for calc fundamentals review.

  • @samarthsai9530
    @samarthsai9530 7 років тому +3

    A BIG ,BIG THANKS with an immense amount of respect to Mr.Patrick.
    I am in 8th grade and love quantum physics,the need of calculus and all of maths in physics convinced me to love maths including calculus and your videos are awesome and super helpful for me.Thanks a lot Sir.

  • @TehraByte
    @TehraByte 9 років тому +44

    i remember doing this with u and v though :/

  • @swade98
    @swade98 12 років тому

    Very informative. Useful reminders for a upcoming Calculus exam.

  • @Xmegan06
    @Xmegan06 10 років тому +7

    You explain everything so well! Why can't you come to my high school to teach calculus?

  • @94bahastbechar
    @94bahastbechar 13 років тому

    your 8 minutes explanation is much more understandable than 2 whole lessons! :) thanksss

  • @michaelcowan1761
    @michaelcowan1761 7 років тому

    Relearning Calculus for a course this Summer. Your videos still hold up 2 years later.

  • @Salamero500
    @Salamero500 13 років тому

    great video, I used to believe I had a learning disability that prevented me from learning this material, but now I can safely say with your help this information has become enjoyable and fun to learn, thank you.

  • @mypinkdollprincess
    @mypinkdollprincess 14 років тому

    You make learning math so much fun and easy and way uncomplicated! I wish all the math teachers/profs teach like you! Thank you!

  • @tijuanamarisol666
    @tijuanamarisol666 13 років тому +2

    i love these videos, they're the only thing keeping me alive in my calc class

  • @rad0ri
    @rad0ri 10 років тому +6

    that first statement just cleared this whole thing up lol

  • @bluebullet89
    @bluebullet89 15 років тому

    WOW!!!! my professor does not explain it even this well. Thanks man LIFESAVER!!!

  • @pageerror404
    @pageerror404 14 років тому

    You should write a book. It's amazing how you make this stuff seem so easy when my professor makes it so difficult.

  • @sh1ft15
    @sh1ft15 10 років тому

    Our lecturer teach us using the substitution method which I find very confusing.Really glad that there is simpler method.Thanks Bro!

  • @bigblue0416
    @bigblue0416 12 років тому

    the only reason i get A's on my Calc. tests are because of you. I dont understand how my teacher teaches us but you make it so simple. THANKS

  • @hdwe1756
    @hdwe1756 7 років тому

    Thanks so much! I really like maths but get bored in school - your videos are an awesome place to learn really interesting concepts and you make everything seem really simple!

  • @frankcastle8129
    @frankcastle8129 7 років тому

    You have no idea how helpful your videos were back in college. 🙏

  • @TracyAlbers23
    @TracyAlbers23 7 років тому +1

    Hi PatrickJMT! Thanks for your videos. This video might be nearly 10 years old but It is still very helpful. I just signed up to contribute to you on Patreon because you have helped me so much. :)

    • @patrickjmt
      @patrickjmt  7 років тому +1

      thanks tracy! i appreciate your support on patreon :)

  • @skylinrcr01
    @skylinrcr01 9 років тому

    Thank you so much for making these videos. They helped me out immensely in Calc, and I really do appreciate you uploading them. Seriously. Thanks.

  • @azndarkdrgn
    @azndarkdrgn 15 років тому

    patrick, I don't know how to say this any other way.
    Your teaching method is short, sweet, and definitely helpful! Keep it up! :D

  • @patrickjmt
    @patrickjmt  14 років тому

    @Seedofwinter if you have variables multiplied by variables, you have to use product rule.

  • @dahuckinator91
    @dahuckinator91 14 років тому

    Man you have no idea how grateful i am to you lol i was doing this wrong and you helped me clean it up. my teacher has a doctorate in math and he always does steps in his head and me being a student in his class i dont know what the heck is going on so i just wanted to thank you for elaborating on this

  • @victoriamayfield5484
    @victoriamayfield5484 7 років тому

    Thank you so much! For some reason I couldn't understand this when my tutor tried to explain it to me, but I totally get the rules when you explain it! You just saved me!!

  • @patrickjmt
    @patrickjmt  16 років тому +1

    try taking the derivative of x^2 normally, and then bust it up and try your rule and see what would happen!

  • @semisikaufusi2467
    @semisikaufusi2467 8 років тому

    GOT IT...Book also supports and thoroughly go over it...the session in class was a little too fast, but now i got it. Thanks. :)

  • @BossMagnus
    @BossMagnus 12 років тому

    man!! you are my hero.. i wish you're my prof.. this is now where im studying.. thanks

  • @awells88
    @awells88 15 років тому

    He teaches calculus to thousands a day. What a teacher. ;)

  • @cubencis
    @cubencis 16 років тому

    derivative of cosine is -(neg)sine, derivative of sine is cosine; every fourth derivation of sine will lead you right back to sine. because of tangent's unique relationship with sin& cosine, you really only need to remember that, tangent= sin/cos (= sine divided by cosin) and cotan is the reciprocal- cos/sin-- so derivatives of each tan argument are the derivatives of sin and cos

  • @patrickjmt
    @patrickjmt  14 років тому

    @FireSign27 product rule has a plus, quotient rule has a negative

  • @agisaraphael5945
    @agisaraphael5945 6 років тому

    I love the way you express these equations. Keep it up

  • @mayz5293
    @mayz5293 13 років тому

    ugh! I want my tuition back... give it mr. patrick... you're a better teacher than my professor...

  • @patrickjmt
    @patrickjmt  14 років тому

    @doggybiscuits89 a binomial is a polynomial

  • @patrickjmt
    @patrickjmt  12 років тому

    glad i could help you for so long :)

  • @bugriyev111
    @bugriyev111 15 років тому

    THANK YOU BROTHA!!! YOU THE MAN! NO REALLY YOUR THE BEST. I love your videos they are so simple easy to see and easy to follow.. nothing more and nothing more.. I love yo style, brotha. Oh! and thank you for being so polite for saying "exuse me" or whatever. thank you!

  • @patrickjmt
    @patrickjmt  17 років тому

    glad i could help you out my friend!

  • @Tyme1v1aster
    @Tyme1v1aster 16 років тому

    If you had 5x^4+8x you could factor and do the product rule. But it'd be easier to just use the power rule.
    4(5)x^3+8x^0 vs.
    1(5x^3+8) + x(3(5)x^2+0)
    Either way you get 20x^3+8

  • @verx666
    @verx666 13 років тому

    Thank you very much for clearing all my doubts patrickJMT, your lessons are short and sweet and it hits the important points :D

  • @xExiledBaconx
    @xExiledBaconx 11 років тому

    His voice. It's...so soothing.

  • @RamiNajjar
    @RamiNajjar 13 років тому

    Excellent handwriting, it really helps!

  • @gordonziegler551
    @gordonziegler551 7 років тому

    PatrickJMT master race, all other tutors are obsolete

  • @henrysprout7506
    @henrysprout7506 7 років тому

    I'm proud of myself for realizing that the sinxcosx part could also be derived using the chain rule and trig identities

  • @Mik_Pick
    @Mik_Pick 12 років тому

    I wish I found these videos before my math test last week...

  • @TJBwestlake
    @TJBwestlake 9 років тому

    i have a test tomorrow, this will help me lots

  • @niallgeraghty200190
    @niallgeraghty200190 15 років тому

    He makes it sound so easy
    great video

  • @guamianki7786
    @guamianki7786 11 років тому

    'cause by the power rule for finding derivatives, X^n = nX^(n-1) so if f(x)=x^3+4, f'(x) would be expressed 3X^(3-1) + 4((0)X^(0-1). So the final result would be: 3X^2 + 0... I think

  • @savindhiparanavitane6478
    @savindhiparanavitane6478 8 років тому

    Your vids really help me cause you explain everything so well! thank you!

  • @sonalram
    @sonalram 13 років тому

    thnks man, ur actually better then most teachers :)..

  • @jonnymoss2488
    @jonnymoss2488 15 років тому

    fucking legend! you've taught me in 8mins 3secs what its taken a maths lecturer a whole term!

  • @JenGutierrez28
    @JenGutierrez28 13 років тому

    Thank you! You make it REALLY easy! My textbook COMPLETELY threw me off! Thanks! :)

  • @grheeinhawaii
    @grheeinhawaii 16 років тому

    thanks for the help dude you are super good at teaching this stuff

  • @sallauddin1
    @sallauddin1 7 років тому

    a big thanks very encouraging tone of voice

  • @levidevison8219
    @levidevison8219 5 років тому

    Thank u so much!
    without ur videos, i’d probably fail every math exam

  • @off-sixk
    @off-sixk 11 років тому

    Thanks for your help!I forgot about calculus, and, you helped me a lot.

  • @trinirougue
    @trinirougue 11 років тому

    thank you sir coming all the way from the caribbean

  • @perfect01011
    @perfect01011 15 років тому

    Thanks! I was absent and missed this lesson. Great explanation.

  • @SnowflurryRavecoon
    @SnowflurryRavecoon 13 років тому

    Hey! Would you mind if i showed this video to a group of kids who are struggling in Calculus class? I can do the material myself by explaining it is where i lose everyone and this video pretty much says it all w/o over complicating things

  • @Maroonsupporter
    @Maroonsupporter 12 років тому

    Thanks for your help. Now I understand how to use the product rule with sine and cos :)

  • @angelatzw1503
    @angelatzw1503 9 років тому +37

    The only guy who makes videos about calculus easy to understand. Khan academy sucks

    • @jasonqhilag8709
      @jasonqhilag8709 8 років тому +3

      true! i hardly understand some topics.

    • @yurikpikh28
      @yurikpikh28 6 років тому

      Agree

    • @Hugs_4_Bugs_
      @Hugs_4_Bugs_ 6 років тому

      @@yurikpikh28 Khan Academy is more for people trying to 'brush up' on a topic. If you know nothing about the topic, he'll leave you in the dust. I don't recommend KA if you're completely lost in the subject, only if there's like a certain thing you don't quite understand.

    • @Pete-Prolly
      @Pete-Prolly 6 років тому +1

      I think PatJMT, Khan, and 3Blue1Brown each bring their own game.
      If you want to pass the test watch PatJMT,
      if you want to understand the intuition and not forget everything you learned right after the test watch Khan,
      if you want to understand the concepts and visualize it watch 3Blue1Brown,
      and if you actually appreciate Math and are serious about it you'll watch all 3 guys and then maybe...maybe this will all make sense to you and you'll retain it.

  • @peteyhopkin
    @peteyhopkin 13 років тому

    cheers mate! helping me witih my engineering maths at uni !!

  • @FanOfAllThingsAwesom
    @FanOfAllThingsAwesom 12 років тому

    You, sir, are simply amazing. Thank you for all the help you've given me! :D

  • @discuss2130
    @discuss2130 10 років тому

    Nice clear explanation. Excellent work.

  • @Lucerozeus
    @Lucerozeus 11 років тому

    it makes a lot of sense. Thanks patrick

  • @patrickjmt
    @patrickjmt  15 років тому

    glad they are helping you : )

  • @JKsisters22
    @JKsisters22 10 років тому +1

    You are awesome ! Thanks a lot, hopefully I'll make it on my test !

  • @akramiexpressconstructionc7113
    @akramiexpressconstructionc7113 9 років тому

    Very good solution for this question

  • @patrickjmt
    @patrickjmt  13 років тому

    @sweetblackstarx takes practice is all.

  • @patrickjmt
    @patrickjmt  16 років тому

    both!

  • @_Jurj
    @_Jurj 8 років тому +12

    maybe ill pass my test tomorrow!

    • @patrickjmt
      @patrickjmt  8 років тому +10

      +David Weeks good luck! Make sure to practice and not just watch :)

    • @librawoman8159
      @librawoman8159 8 років тому

      David Weeks maybe I will as well

  • @patrickjmt
    @patrickjmt  15 років тому

    cos^2X - sin^2X = -1(cos^2X + sin^2X) is not correct

  • @zdsfgdsfhgdhnzdhn
    @zdsfgdsfhgdhnzdhn 13 років тому

    are you getting paid for all these videos? or at least getting paid for teaching math? you are by far better than many many math teachers, and you could easily have a teaching profession. Keep it up dude!

  • @RoodyRoo
    @RoodyRoo 9 років тому

    Question. Probably buried somewhere in the comments. In the last problem, he used the product rule within f(x) because sinx and cosx were being multiplied within the parenthesis?

  • @sapphir3ros383
    @sapphir3ros383 15 років тому

    you make things so easy to understand! =) thank you so so much!

  • @kellyanderson4910
    @kellyanderson4910 4 роки тому

    This was so helpful. Subscribed

  • @garangjok7552
    @garangjok7552 7 років тому

    Thanks for neat information JMT

  • @viewsfromthepit
    @viewsfromthepit 15 років тому

    thanks so much!
    you are one hell of a teacher

  • @Jukoe08
    @Jukoe08 15 років тому

    when are you supposed to use product rule over a quotient rule if you have to multiply and divide (x+1)(x-2)/(x^2+1)

  • @RunTooFree
    @RunTooFree 15 років тому

    hey pat, 1st of all, I love all your videos, and thanks for sharing your knowledge to the world!
    Question on the last example: can you just take derivative of each parts? like this y' = (cosx)(cos)(x²+1) + (sinx)(-sinx)(x²+1) + (sinx)(cosx)(2x) ?
    Also, when i enter d(sin(x)cos(x)(x^2+1),x) and my TI-89 shows (2·x²+2)(cos(x))²+2·x·sin(x)·cos(x) - x² - 1

  • @TBBuccaneers1717
    @TBBuccaneers1717 14 років тому

    I just watched your quotient rule vid then this. seriously... you should be a teacher. I just learned derivatives in 5 minutes. I loveeeeeee you. (not in a creepy way :D)

  • @boorens18
    @boorens18 15 років тому

    you should strongly consider teaching calculus...you'll save lives

  • @Pete-Prolly
    @Pete-Prolly 6 років тому +1

    y = f(x)•g(x)•h(x)
    y' = f'gh + fg'h + fgh'
    works too
    (not saying either way is better so please don't troll me for trying to help)

  • @salohaap8140
    @salohaap8140 4 роки тому

    thank u sr for making the video more understandable

  • @hadleyarco7066
    @hadleyarco7066 6 років тому +23

    Anyone watching in 2019?