Derivative of Sine and Cosine Functions | Calculus

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  • Опубліковано 6 жов 2024
  • This calculus video tutorial explains how to find the derivative of sine and cosine functions. it explains why the derivative of sine is cosine using the limit definition of the derivative.
    Derivatives - Fast Review: • Calculus 1 - Derivatives
    Limit Definition of the Derivative:
    • Definition of the Deri...
    Derivatives - Alternate Limit Definition:
    • Alternate Form of The ...
    Derivatives - The Constant Rule:
    • The Constant Rule For ...
    Derivatives - The Power Rule:
    • The Power Rule For Der...
    _________________________________
    Derivatives - Constant Multiple Rule:
    • The Constant Multiple ...
    Derivatives - Polynomial Functions:
    • Derivatives of Polynom...
    Derivatives - Sine and Cosine:
    • Derivative of Sine and...
    Derivatives - Trigonometric Functions:
    • Derivatives of Trigono...
    Derivatives - Limits:
    • Limits and Derivatives
    _______________________________________
    Equation of the Tangent Line:
    • How To Find The Equati...
    Derivatives - Horizontal Tangent Line:
    • How to Find The Point ...
    The Equation of The Normal Line:
    • How To Find The Equati...
    The Equation of The Secant Line:
    • How To Find The Equati...
    Average and Instantaneous Velocity:
    • Average Velocity and I...
    _______________________________________
    Final Exams and Video Playlists:
    www.video-tuto...
    Full-Length Videos and Worksheets:
    / collections
    Derivatives - Formula Sheet:
    bit.ly/4dThzf1

КОМЕНТАРІ • 85

  • @TheOrganicChemistryTutor
    @TheOrganicChemistryTutor  Рік тому +6

    Derivatives - Formula Sheet: bit.ly/4dThzf1
    Final Exams and Video Playlists: www.video-tutor.net/
    Next Video: ua-cam.com/video/PEqCa0U77mc/v-deo.html

  • @anneliese8845
    @anneliese8845 4 місяці тому +8

    My body was shaking, i felt sick to my stomach, my hands were trembling bc i literally did not understand ANYTHING from my lectures. You my guy saved my life today ❤

  • @tasniarahman4407
    @tasniarahman4407 3 роки тому +205

    This man is saving lives everyday.

  • @oguzhanalasulu5678
    @oguzhanalasulu5678 2 роки тому +36

    Proving method is absolutely more logical than the memorizing something. I'd like to present our thanks on behalf of your genuine videos for us, Professor.

  • @adalhernandez8105
    @adalhernandez8105 2 роки тому +26

    It is unbelievable that this guy explains better than my professor with a PhD

  • @DaiMoscv
    @DaiMoscv 3 роки тому +13

    I have taught all these when I was in high-school but now I have to relearn for the college and these videos are so simple and comprehensive. Thank you for your hardwork, keep it coming!

  • @illbetherichest
    @illbetherichest 6 років тому +60

    Im still watching your videos even though Ive graduated from college

    • @gartyqam
      @gartyqam 4 роки тому

      u must be dumb if u are still watching derivative questions at like 22 years old and i learned about this when i was 17 years old

    • @gartyqam
      @gartyqam 4 роки тому +2

      i learned this in high school while u learned this in graduate school, u are slooow

    • @Pikachu-xg7st
      @Pikachu-xg7st 4 роки тому +40

      haha derp stfu, everyone struggles in a different area. As long as the person understands the concept, thats all that matters regardless of age. don't think you're superior just cause u learned it at 17. Im learning it at 16 so be humble. Everyone learns at a different pace dipshit

    • @WhateverOwO
      @WhateverOwO 3 роки тому +12

      @@gartyqam I mean, I learnt it at 14 sooooo, also stfu you are not more intelligent than other people just by understanding one thing in mathematics at a young age

    • @gartyqam
      @gartyqam 3 роки тому

      @@Pikachu-xg7st no u stfu, a few months gap is nothing for you to have jumped to that conclusion also difference between 17 and 22 shows a lack of intelligence and 16 and 17 have no difference thanks noob for making urself look foolish

  • @LloydSMITH
    @LloydSMITH 3 роки тому +10

    Very simple Actually !

    • @primalpiano7580
      @primalpiano7580 3 роки тому +4

      Lloyd Smith you have the coolest channel !

  • @georgesadler7830
    @georgesadler7830 Рік тому

    MR. Organic Chemistry Tutor, this is an awesome topic on Finding the derivatives of two well-known Transcendental functions in all of Mathematics, Physics and Engineering.

  • @benedictelgamal9174
    @benedictelgamal9174 3 роки тому +1

    Thanks so much I do love your lectures, sweet maths Enjoying from Kenya

  • @chaenglaurent11
    @chaenglaurent11 6 років тому +16

    Damn. Man. That was lit as hell

  • @renewd
    @renewd 4 роки тому +11

    Now, let's all prove that the dervative of cos(x) is - sin(x) in the same way.

  • @bigguy1107
    @bigguy1107 2 роки тому

    Thank u very much. I like your delivery

  • @alexendalew
    @alexendalew 7 місяців тому +1

    this video is posted 6 years ago and i am enjoying it in 2024

  • @kurdistanhomeschool4471
    @kurdistanhomeschool4471 6 років тому +2

    Excellent!!!

  • @belladigregorio4972
    @belladigregorio4972 Рік тому

    Thank you this helped a lot

  • @diothepoet7311
    @diothepoet7311 3 роки тому

    Life saver this one, I love like him❣️

  • @Pedoraruba304
    @Pedoraruba304 Рік тому +1

    This is basically A free College course Channel

  • @DxD_Primus
    @DxD_Primus 4 роки тому +1

    Thank you it really helped me

  • @dewmihennayake3428
    @dewmihennayake3428 3 роки тому

    Ammooh for the past three years i felt this is a hell and now in one day i feel theres' nothing😂😂💔. Damn thans for the job man you made maths really nice 🔥

  • @vampirebynight6417
    @vampirebynight6417 6 років тому +5

    it was all good until you tried to prove the derivative of sinx is indeed equal to consinex. I don't think that's something very important to know early on when learning these things and i also feel like i would've benefited from more harder examples instead of that.

    • @justinsantos5751
      @justinsantos5751 5 років тому +1

      If you are aiming for high grades only then I don't think it's important too, but if you want to understand calculus better then I think it's very important.

    • @Phantom_Kraken
      @Phantom_Kraken 4 роки тому

      the first page of this section in my text book starts by providing the derivative of sinx is cos

  • @henrychikuni9599
    @henrychikuni9599 2 роки тому

    your the best sir😍🤩

  • @suzdls3626
    @suzdls3626 2 роки тому

    I'm literally doing this before mew year!!!

  • @dougr.2398
    @dougr.2398 3 роки тому +1

    The initial focus here is not on deriving the derivative. The crux of the matter is the two limits. That these must be in radians and not degrees is neglected, as usual.

    • @mathgod_au2503
      @mathgod_au2503 Рік тому

      I explain the 2 relevant limits more 'properly' in my video: ua-cam.com/video/vhXG3GP2_HE/v-deo.html
      Checked it after reading your comment and I did in fact very quickly mention radians!

  • @Saad_LH
    @Saad_LH 3 місяці тому

    Love you bro ❤

  • @zaza-yp2kl
    @zaza-yp2kl 2 роки тому

    i love you thank you so much

  • @parsasamandi569
    @parsasamandi569 3 місяці тому

    Good job

  • @gangstergaming2974
    @gangstergaming2974 2 роки тому

    Love from India 🇮🇳

  • @rehabzeidan3052
    @rehabzeidan3052 3 роки тому

    Is (sin(a+b)=sin a cos b + cos a sin b) constant rule??

  • @DIVINEONWUKA-o7g
    @DIVINEONWUKA-o7g 10 місяців тому

    I am confused though... I tried proving the trigonometric functions listed and i was getting neither 1 or 0. Please explain. Maybe i am missing something

  • @pukitaki
    @pukitaki 4 роки тому +1

    Dude, you did your proof backward.
    The limit as "h" approaches zero of (1-cos(h))/h DOES NOT equal zero, it's supposed to be the limit of (cos(h)-1)/h that equals zero.
    It may not look like a big difference to most people, and because it does equal 0, you don't notice the difference whether you're factoring out a positive or negative sine, but it will make a huge difference in other problems. Please post a correction!

    • @gartyqam
      @gartyqam 4 роки тому +4

      ok karen

    • @trubblman
      @trubblman 3 роки тому +2

      @@gartyqam Pukitaki is right though

    • @nexypoo
      @nexypoo Рік тому

      Pukitaki is wrong, as he factored out a -1..

  • @HACKER-oc7du
    @HACKER-oc7du 2 роки тому

    Thankss👏👏

  • @jessicajiang8028
    @jessicajiang8028 4 роки тому +1

    How do i answer a question that asks me to find the 45 derivative of cosx

    • @Toolace
      @Toolace 3 роки тому +1

      I know I'm waaaay late, but I believe the answer to that question would be "45 - sin x"

    • @Tza-mri
      @Tza-mri 3 роки тому

      Perhaps its -45sinx. 😅

  • @afikangubane7045
    @afikangubane7045 Рік тому

    9:05 why must it be in radial mode

  • @ms25ll
    @ms25ll Рік тому

    2:41 if I put -3.14 is true ?

  • @Dippa1991
    @Dippa1991 5 років тому +1

    What if it’s cos4x ?

    • @justinsantos5751
      @justinsantos5751 5 років тому +5

      You need to use chain rule. I believe the answer is (-sin4x)(4)= -4sin4x
      Correct me if I'm wrong, it's been a year since my last calculus class

  • @samiulislamdurjoy
    @samiulislamdurjoy 3 роки тому

    G 214

  • @nikite_9289
    @nikite_9289 3 роки тому

    3:36 is a real flip 😂

  • @naimatullahkhanitistruth5062
    @naimatullahkhanitistruth5062 4 роки тому

    You don't discuss about its graphically

  • @wiwikawaii473
    @wiwikawaii473 5 років тому

    Whats the der of f(x) = x +xcosx

    • @colinp8918
      @colinp8918 4 роки тому

      wiwi kawaii 1+cosx - x sinx

    • @wiwikawaii473
      @wiwikawaii473 4 роки тому

      @@colinp8918 tnx😻❤

    • @wiwikawaii473
      @wiwikawaii473 4 роки тому

      @@colinp8918 can u show me the method plz??

    • @JKMath
      @JKMath 2 роки тому

      @@wiwikawaii473 He used the product rule for the second term of the function, so the derivative looks like this: 1 + x*(-sinx) + cosx*1. Then after simplifying, that would equal the answer Colin gave you of 1 + cosx -xsinx. Hope that helps!

  • @뉴욕커-d2x
    @뉴욕커-d2x 4 роки тому +1

    how do you differentiate z=4cos(t^t)? please let me know, I have no idea how to deal with the function in the parenthesis, t^t

    • @Phantom_Kraken
      @Phantom_Kraken 4 роки тому +1

      Did you ever figure it out?

    • @Thorngot
      @Thorngot 3 роки тому +2

      I don't think they did.

    • @JKMath
      @JKMath 2 роки тому +2

      Assuming you are looking for dz/dt, or the derivative of z with respect to t, you have a pretty complex chain rule derivative here. The first part would be -4sin(t^t), and then you would multiply this by the derivative of t^t (the inside function), which is tricky. It would be the same as taking the derivative of x^x, which I have made a video for that you can check out: ua-cam.com/video/O99L3G08ubQ/v-deo.html
      Hope that helps!

  • @mathgod_au2503
    @mathgod_au2503 Рік тому

    I find OCT videos helpful for showing the HOW to do problems but re-viewed this video and noticed that he does the limits the 'handwavy' way.
    If you're interested in the WHY of the 2 limits they're explained in my video here: ua-cam.com/video/vhXG3GP2_HE/v-deo.html

  • @thatomofolo452
    @thatomofolo452 Рік тому

  • @somad5773
    @somad5773 5 років тому

    Wow!

  • @otakusensei132
    @otakusensei132 3 роки тому

    Omg men. the last part is like what the hell happened?

  • @alterego480
    @alterego480 4 роки тому

    yo this guy is mark wahlberg but young

  • @SweetShandyDuquesa
    @SweetShandyDuquesa Місяць тому

    pls sana makapasa ako bukas

  • @Chrisymcmb
    @Chrisymcmb 3 роки тому

    Noiceeeee

  • @كمالالدينعليعباس
    @كمالالدينعليعباس 2 роки тому

    تاتا

  • @DoubleA_Monk13
    @DoubleA_Monk13 Рік тому

    子にちわ