Inverse trig functions derivatives

Поділитися
Вставка
  • Опубліковано 17 жов 2024
  • Here we will prove the derivatives of all the inverse trigonometric functions. The main tool to find the inverse trig functions derivatives is implicit differentiation. These results are very important for your calculus classes. Note: the notation sin^-1(x) means the inverse sine or arcsin(x). Sin^-1(x) is very different than (sin(x))^-1.
    0:16 derivative of inverse sin(x), derivative of sin^-1(x)
    3:41 derivative of inverse tan(x), derivative of tan^-1(x)
    6:12 derivative of inverse sec(x), derivative of sec^-1(x)
    9:20 derivative of inverse cos(x), derivative of cos^-1(x)
    11:02 derivative of inverse cot(x), derivative of cot^-1(x)
    12:14 derivative of inverse csc(x), derivative of csc^-1(x)
    If you want to see a "fast" version, check out this video: • Derivatives of All INV...
    ---------------------------------------------------------
    This channel is dedicated to students who are taking precalculus, AP calculus, GCSE, A-Level, year 12 maths, college calculus, or high school calculus. Feel free to leave calculus questions in the comment section and subscribe for future videos.
    Subscribe by clicking 👉 bit.ly/just_calc
    ---------------------------------------------------------
    If you find my channel helpful and would like to support, then please check out
    My Patreon: 👉 / blackpenredpen
    My merch store: 👉 bit.ly/bprp_merch

КОМЕНТАРІ • 83

  • @rationalcommentor
    @rationalcommentor 10 місяців тому +14

    Man just simplified and showed where the formula came from. Kudos

  • @marioluigijam3612
    @marioluigijam3612 2 роки тому +80

    WHY couldn’t my calc prof explain inverse trig derivatives like this? She made it much more confusing. You make it seems like something I could have figured out on my own.😊

    • @overlord3481
      @overlord3481 4 місяці тому +1

      the problem was that she was a female teaching maths

    • @moocow3541
      @moocow3541 4 місяці тому

      @@overlord3481 ?

    • @chriswellnitz
      @chriswellnitz 23 дні тому

      ​@@overlord3481 ew cringe take

    • @Nyxie405
      @Nyxie405 19 днів тому

      ​@@chriswellnitz Almost every female math teacher sucks

  • @neilgerace355
    @neilgerace355 3 роки тому +50

    10:25 Two angles that add up to π/2 are said to be complementary. That's where the co in cosine, cotangent, cosecant comes from.

  • @ChrisP999
    @ChrisP999 3 роки тому +28

    Couldnt have a better timing with my cal 1 class now that I'm comfortable with the trig derivatives. Thank you!

  • @vinzxd3114
    @vinzxd3114 Місяць тому +3

    I already read this via implicit derivativez but you expained it better. You always number 1 to me Sir. Thankyou

  • @abehankens7456
    @abehankens7456 19 днів тому

    thank you, my calc teacher gave no explanation as to how these derivatives are derived and simply told us to memorize them, this is quite helpful

  • @abeloiscauchy8009
    @abeloiscauchy8009 Рік тому +3

    My man did the great job!
    After watching the derivatives of arcsin,I did all the rest of derivative of inverse tri functions on my own becuz I already have similar idea before. Btw,This informative video makes my mind clear and dawn upon my imaginations.
    -wondering why you are so underrated.

  • @lstrike6964
    @lstrike6964 3 роки тому +10

    Great video! Could you please also show the derivatives for hyperbolic and inverse hyperbolic trig functions? Thanks

  • @wolfgangpauli4489
    @wolfgangpauli4489 7 місяців тому +3

    One should use arcsin and so forth. That is the way it is done in all non-English speaking countries. The notation sin^-1 can be confused with (sin X)^-1.

  • @ThimmegowdaNM
    @ThimmegowdaNM 2 місяці тому

    Dear sir really Your way is helpful to the beginner students.

  • @Tejshree.Meshram
    @Tejshree.Meshram 3 місяці тому

    I just love the way you change markers while writing without being noticed. It feels so cool. However, why do you hold that pokeball throughout the lecture?

  • @justabunga1
    @justabunga1 3 роки тому +5

    I know that for derivatives of arcsec(x) and arccsc(x) was supposed to have an absolute value around the x in most textbooks since you said that it depends on the domain, but when you derive using the proof, how do you get that one with the absolute value?

    • @bprpcalculusbasics
      @bprpcalculusbasics  3 роки тому

      Unfortunately I do not have the time to make a video now. But I made a post, please see here ua-cam.com/channels/MUu2lQ_ilNsb26oWrc5ENw.htmlcommunity?lb=UgzaLm2NcjWufD5E6YB4AaABCQ

  • @SammaS14owo
    @SammaS14owo Рік тому

    看不懂stewart老師的微積分跑來這裡
    謝謝曹老師 這解釋真的更容易理解了

  • @SoftMbuzi
    @SoftMbuzi Місяць тому

    You have really fed my brain sir thanks 👍 so much

  • @arimermelstein9167
    @arimermelstein9167 3 роки тому +7

    Here I go again. I know that I just told you that I’m not bothered by notation, but I guess there’s an exception to that rule. I much prefer the arc*** notation rather than the -1 notation.

    • @bprpcalculusbasics
      @bprpcalculusbasics  3 роки тому +8

      I agree the arc something notation is better. It’s just a bit too long to write them. 😆

    • @sabkobds
      @sabkobds 2 роки тому +1

      ​@@bprpcalculusbasics As el. engineer, for me is sin^-1(x)=1/sin(x). Because we use all the time, for example, sin^2(x).
      I know about this notation too, of course, but it was a little bit confusing at the beginning.
      If it is just some random function f, than I would never think about f^-1 as something other than inverse function.
      It must be hardcoded in my brain during education...

  • @glowmobile596
    @glowmobile596 3 роки тому +1

    I love this channel so far! Keep it up man

  • @ReTautica
    @ReTautica 2 роки тому +2

    That made it so much easier to remember.

  • @SeanBenson23
    @SeanBenson23 3 роки тому +1

    Oh my God, this is life changing

  • @Jy3388
    @Jy3388 2 роки тому

    now i know how they come up with all those formulars, thanks

  • @mohamedsalam5496
    @mohamedsalam5496 3 роки тому +2

    Can you please do a video about Improper Integrals - Convergence and Divergence? your video helped me a lot in my last quiz and this week on Thursday I have this topic

    • @bprpcalculusbasics
      @bprpcalculusbasics  3 роки тому +2

      Here’s a video on them ua-cam.com/video/sjlZ_KX3cqM/v-deo.html

  • @EyeSooGuy
    @EyeSooGuy 7 місяців тому

    Hey Steve! You should ELI5 on what analytic geometry and analytic trigonometry are.

  • @persiusathena336
    @persiusathena336 10 місяців тому

    More easier to listen to, thanks sir!

  • @cosmicvoidtree
    @cosmicvoidtree 3 роки тому +1

    Cool video. I’ve been trying to work on the derivative of the inverse of the error function (but scaled by 2/sqrt(pi) to remove the constant from the definition) and I got to dy/dx=e^y^2. Unfortunately getting y is annoying so I decided to move on. If you want to try it for a video that would be cool.

  • @ramoncastillo532
    @ramoncastillo532 7 місяців тому

    you are great at explaining great video

  • @OllorJohn-kr7so
    @OllorJohn-kr7so Рік тому

    Please sir , am so joyous after watching your video, please tag me each time you post a new video .Am John Ollor from Ghana thanks

  • @MilanPrajapati-o1e
    @MilanPrajapati-o1e 9 місяців тому +1

    hint you can rewrite arcsec(x)=arccos(1/x), arccsc(x)=arcsin(1/x), arccot(x)=arctan(1/x) make sure to use u substitution for inverse trigs hope this is helpful

  • @user-wu8yq1rb9t
    @user-wu8yq1rb9t 3 роки тому +1

    Hello teacher
    I love your sensitivity about your work ( the picture should be nice). It shows us how you respect for your work (actually Math) and your audience.
    Thank you so much teacher

  • @elijahhsu1192
    @elijahhsu1192 6 місяців тому

    For tan^-1(x), I didn't learn implicit diff. but I did learn e^(i*x)=cos(x) + i*sin(x). so I found the complex function for tan^-1(x) and made my life so much harder by differentiating that XD

  • @itsohaya4096
    @itsohaya4096 Рік тому +1

    My calc teacher just skipped over this and gave us the derivatives On a piece of paper :(((
    Thanks black pen red pen

  • @arthurzaneti-cx2en
    @arthurzaneti-cx2en Рік тому +2

    Great video man

  • @SaifulIslam-id1rt
    @SaifulIslam-id1rt 11 місяців тому

    Big fan sir, 🇧🇩 🇧🇩 💕

  • @NurbolBelyal
    @NurbolBelyal 11 місяців тому

    Wow awesome, explanations sir!

  • @charlesbrown6250
    @charlesbrown6250 Місяць тому +1

    Just saved my life very well explained thank you so much 😅

  • @ابولفضلجهانی-ص2و

    very cute explanation 🤩

  • @sarthakgupta2463
    @sarthakgupta2463 Місяць тому

    Superb

  • @abdalrhmansallam3119
    @abdalrhmansallam3119 Рік тому

    He really kept holding the Pokémon ball, what a legend

  • @ezraclark1793
    @ezraclark1793 Місяць тому

    thank you so much!

  • @faithwangui7200
    @faithwangui7200 Рік тому

    What is the ball for? Just curious

    • @lumina_
      @lumina_ Рік тому +1

      for style 😎

    • @brayton6683
      @brayton6683 Рік тому +1

      He's actually holding a mic 🎤

  • @danieltambunan9717
    @danieltambunan9717 2 роки тому +1

    9:53 i dont understand why the angel is sin^-1 (x) . Any one can explain?

    • @hydropage2855
      @hydropage2855 2 роки тому +3

      It's because sin^1(x) means "the angle whose sine is x", and x = x/1. So opposite = x, and hypotenuse = 1, like the triangle he drew

    • @danieltambunan9717
      @danieltambunan9717 2 роки тому

      @@hydropage2855 OH YEAH YOU'RE RIGHT. Hahaha i was just so confuse with myself

  • @rajpandya3766
    @rajpandya3766 2 роки тому

    this helps so much ty

  • @prashishdahal9605
    @prashishdahal9605 2 роки тому +2

    I came here from your other calculus video and I got scared by your beard.

  • @kshytij2066
    @kshytij2066 4 місяці тому

    you are the goat

  • @حامدعبدالفتاح-ت1ض
    @حامدعبدالفتاح-ت1ض 5 місяців тому +2

    يوم الثلاثاء علي امتحان في التفاضل و التكامل 2 اتمنى ان احصل على العلامت الكامله 😅

    • @multimeme5935
      @multimeme5935 4 місяці тому +1

      ابشر؟

    • @حامدعبدالفتاح-ت1ض
      @حامدعبدالفتاح-ت1ض 4 місяці тому +1

      @@multimeme5935 حصلت على علامة كامله شكرا لسائلك هاذا من لطفك
      ظننت اني العربي الوحيد الذي يتابع هاذه القنات 😅

    • @حامدعبدالفتاح-ت1ض
      @حامدعبدالفتاح-ت1ض 4 місяці тому

      ​@@multimeme5935
      لقد حصلت على العلامة الكاملة شكراً لسائلك
      هاذا من لطفك .
      ظننت اني الشخص العربي الوحيد الذي يتابع هاذه القنات😅

    • @حامدعبدالفتاح-ص2ف
      @حامدعبدالفتاح-ص2ف 4 місяці тому

      ​@@multimeme5935
      حصلت على العلامت الكاملة شكرا لسائلك هاذا من لطفك .
      ظننت اني العربي الوحيد الذي يتابع هاذه القنات

    • @حامدعبدالفتاح-ت1ض
      @حامدعبدالفتاح-ت1ض 4 місяці тому +1

      @@multimeme5935
      حصلت على علامت كاملة
      شكراً لسائلك هاذا من لطفك.
      ظننت اني العربي الوحيد الذي يتابع هاذه القنات 😅

  • @boboishmael3132
    @boboishmael3132 Рік тому

    Better explanation

  • @madhavkumar6434
    @madhavkumar6434 3 роки тому

    sir I love you soooo much❤️

  • @tanmaydhakate7730
    @tanmaydhakate7730 3 роки тому +1

    Thanks a lot.

  • @SintayehuSiraye-pf8gh
    @SintayehuSiraye-pf8gh Рік тому +1

    thanks bro

  • @molemo9516
    @molemo9516 2 роки тому

    Really good

  • @arimermelstein9167
    @arimermelstein9167 3 роки тому

    I also immediately thought to do 1/(sec^2 y) = cos^2 y.

  • @miax2469
    @miax2469 2 роки тому

    Good job

  • @mrsabraattiaselim5334
    @mrsabraattiaselim5334 Рік тому

    thanks a lot

  • @JuanConsuegra-dw3ie
    @JuanConsuegra-dw3ie Рік тому

    Amazing

  • @litsepisokose9897
    @litsepisokose9897 2 роки тому

    thank you

  • @engyanwer6770
    @engyanwer6770 Рік тому

    perfect👌🏻

  • @t3q4wet3q4e
    @t3q4wet3q4e 8 місяців тому

    i feel stupid for not ever using a right angle triangle
    i just always used cos^2(a)+sin^2(a) = 1 and got stuck whenever it involved functions other than sin and cos

  • @Jose_814
    @Jose_814 Місяць тому

    i love you asian teacher

  • @Useruseruser888
    @Useruseruser888 3 місяці тому

    Thank You * d/dx [1Billion*x] times 😅

  • @muhammadramazanov1751
    @muhammadramazanov1751 Рік тому

    you are so handsome with this beard

  • @auxgamr111
    @auxgamr111 Рік тому

    👍👍👍

  • @Easylearning-cs3ji
    @Easylearning-cs3ji 5 місяців тому

    please cut the haire becouse frithed

  • @epsilonxyzt
    @epsilonxyzt 8 місяців тому

    Talk another language instead of english. Do you understand what you pronounce?

    • @Occ881
      @Occ881 2 місяці тому

      You're rude😢

    • @Occ881
      @Occ881 2 місяці тому

      You need to work on your grammar too😂

    • @albertglai
      @albertglai Місяць тому

      From your typing, you don’t even know proper English. No wonder you don’t understand his English. It looks like you need to brush up your English. I don’t have a problem understanding his pronunciation. It’s you the problem.

  • @mccauleybacalla2228
    @mccauleybacalla2228 Рік тому +1

    thank you so much!