Derivative of Sine and Cosine Functions | Calculus

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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

Опубликовано:

28 сен 2024

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Комментарии : 85

@TheOrganicChemistryTutor Год назад

Derivatives - Formula Sheet: bit.ly/4dThzf1 Final Exams and Video Playlists: www.video-tutor.net/ Next Video: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-PEqCa0U77mc.html

@anneliese8845 4 месяца назад

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 ❤

@oguzhanalasulu5678 2 года назад

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.

@tasniarahman4407 3 года назад

This man is saving lives everyday.

@diothepoet7311 3 года назад

I couldn't agree more buddy, he helped me a lot

@aliaamohamed1754 9 месяцев назад

True my final is tomorrow

@AKT_2001 6 месяцев назад

Exactly

@SandraMwaipopo Месяц назад

True 💯

@DaiMoscv 3 года назад

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!

@bigguy1107 2 года назад

Thank u very much. I like your delivery

@alexendalew 7 месяцев назад

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

@renewd 4 года назад

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

@Pedoraruba304 Год назад

This is basically A free College course Channel

@diothepoet7311 3 года назад

Life saver this one, I love like him❣️

@suzdls3626 2 года назад

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

@DxD_Primus 4 года назад

Thank you it really helped me

@Saad_LH 2 месяца назад

Love you bro ❤

@gangstergaming2974 2 года назад

Love from India 🇮🇳

@rehabzeidan3052 3 года назад

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

@DIVINEONWUKA-o7g 10 месяцев назад

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

@parsasamandi569 3 месяца назад

Good job

@afikangubane7045 Год назад

9:05 why must it be in radial mode

@ms25ll Год назад

2:41 if I put -3.14 is true ?

@Dippa1991 5 лет назад

What if it’s cos4x ?

@justinsantos5751 5 лет назад

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

@كمالالدينعليعباس 2 года назад

تاتا

@DoubleA_Monk13 Год назад

子にちわ

@adalhernandez8105 2 года назад

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

@illbetherichest 6 лет назад

Im still watching your videos even though Ive graduated from college

@gartyqam 4 года назад

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 4 года назад

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

@Pikachu-xg7st 4 года назад

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 3 года назад

@@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 3 года назад

@@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 3 года назад

Very simple Actually !

@primalpiano7580 3 года назад

Lloyd Smith you have the coolest channel !

@chaenglaurent11 6 лет назад

Damn. Man. That was lit as hell

@hige8692 3 года назад

Lol

@benedictelgamal9174 3 года назад

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

@vampirebynight6417 6 лет назад

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 5 лет назад

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 4 года назад

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

@kurdistanhomeschool4471 6 лет назад

Excellent!!!

@SweetShandyDuquesa Месяц назад

pls sana makapasa ako bukas

@henrychikuni9599 2 года назад

your the best sir😍🤩

@thatomofolo452 Год назад

@pukitaki 4 года назад

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 4 года назад

ok karen

@trubblman 3 года назад

@@gartyqam Pukitaki is right though

@nexypoo Год назад

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

@dougr.2398 3 года назад

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 Год назад

I explain the 2 relevant limits more 'properly' in my video: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-vhXG3GP2_HE.html Checked it after reading your comment and I did in fact very quickly mention radians!

@belladigregorio4972 11 месяцев назад

Thank you this helped a lot

@otakusensei132 3 года назад

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

@georgesadler7830 Год назад

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.

@naimatullahkhanitistruth5062 4 года назад

You don't discuss about its graphically

@dewmihennayake3428 3 года назад

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 🔥

@alterego480 4 года назад

yo this guy is mark wahlberg but young

@zaza-yp2kl 2 года назад

i love you thank you so much

@jessicajiang8028 4 года назад

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

@Toolace 3 года назад

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

@Tza-mri 3 года назад

Perhaps its -45sinx. 😅

@nikite_9289 3 года назад

3:36 is a real flip 😂

@HACKER-oc7du 2 года назад

Thankss👏👏

@Chrisymcmb 3 года назад

Noiceeeee

@samiulislamdurjoy 3 года назад

G 214

@somad5773 5 лет назад

Wow!

@wiwikawaii473 5 лет назад

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

@colinp8918 4 года назад

wiwi kawaii 1+cosx - x sinx

@wiwikawaii473 4 года назад

@@colinp8918 tnx😻❤

@wiwikawaii473 4 года назад

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

@JKMath 2 года назад

@@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!

@mathgod_au2503 Год назад

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: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-vhXG3GP2_HE.html

@뉴욕커-d2x 4 года назад

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 4 года назад

Did you ever figure it out?

@Thorngot 3 года назад

I don't think they did.

@JKMath 2 года назад

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: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-O99L3G08ubQ.html Hope that helps!