Inverse trig functions derivatives
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- Опубликовано: 13 окт 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...
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Man just simplified and showed where the formula came from. Kudos
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.😊
the problem was that she was a female teaching maths
@@overlord3481 ?
@@overlord3481 ew cringe take
@@chriswellnitz Almost every female math teacher sucks
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.
Couldnt have a better timing with my cal 1 class now that I'm comfortable with the trig derivatives. Thank you!
I already read this via implicit derivativez but you expained it better. You always number 1 to me Sir. Thankyou
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
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.
Great video! Could you please also show the derivatives for hyperbolic and inverse hyperbolic trig functions? Thanks
You have really fed my brain sir thanks 👍 so much
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?
Dear sir really Your way is helpful to the beginner students.
I love this channel so far! Keep it up man
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.
I agree the arc something notation is better. It’s just a bit too long to write them. 😆
@@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...
That made it so much easier to remember.
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
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.
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?
Unfortunately I do not have the time to make a video now. But I made a post, please see here ruclips.net/channel/UCMUu2lQ_ilNsb26oWrc5ENwcommunity?lb=UgzaLm2NcjWufD5E6YB4AaABCQ
Oh my God, this is life changing
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
More easier to listen to, thanks sir!
you are great at explaining great video
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
Here’s a video on them ruclips.net/video/sjlZ_KX3cqM/видео.html
Hey Steve! You should ELI5 on what analytic geometry and analytic trigonometry are.
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.
now i know how they come up with all those formulars, thanks
Great video man
Just saved my life very well explained thank you so much 😅
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
Wow awesome, explanations sir!
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
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
very cute explanation 🤩
Superb
thank you so much!
this helps so much ty
Big fan sir, 🇧🇩 🇧🇩 💕
Thanks a lot.
My calc teacher just skipped over this and gave us the derivatives On a piece of paper :(((
Thanks black pen red pen
thanks bro
you are the goat
Really good
I came here from your other calculus video and I got scared by your beard.
thanks a lot
He really kept holding the Pokémon ball, what a legend
Good job
sir I love you soooo much❤️
Better explanation
Amazing
thank you
يوم الثلاثاء علي امتحان في التفاضل و التكامل 2 اتمنى ان احصل على العلامت الكامله 😅
ابشر؟
@@multimeme5935 حصلت على علامة كامله شكرا لسائلك هاذا من لطفك
ظننت اني العربي الوحيد الذي يتابع هاذه القنات 😅
@@multimeme5935
لقد حصلت على العلامة الكاملة شكراً لسائلك
هاذا من لطفك .
ظننت اني الشخص العربي الوحيد الذي يتابع هاذه القنات😅
@@multimeme5935
حصلت على العلامت الكاملة شكرا لسائلك هاذا من لطفك .
ظننت اني العربي الوحيد الذي يتابع هاذه القنات
@@multimeme5935
حصلت على علامت كاملة
شكراً لسائلك هاذا من لطفك.
ظننت اني العربي الوحيد الذي يتابع هاذه القنات 😅
perfect👌🏻
What is the ball for? Just curious
for style 😎
He's actually holding a mic 🎤
I also immediately thought to do 1/(sec^2 y) = cos^2 y.
9:53 i dont understand why the angel is sin^-1 (x) . Any one can explain?
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
@@hydropage2855 OH YEAH YOU'RE RIGHT. Hahaha i was just so confuse with myself
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
👍👍👍
i love you asian teacher
Thank You * d/dx [1Billion*x] times 😅
you are so handsome with this beard
please cut the haire becouse frithed
Talk another language instead of english. Do you understand what you pronounce?
You're rude😢
You need to work on your grammar too😂
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.
thank you so much!