Derivatives of Trigonometric Functions

Now that we can take the derivative of polynomial functions, as well as products and quotients thereof, it's time to start looking at special functions, like trigonometric functions. How can we take the derivative of these if we can't use the power rule? Good thing we understand the concept of differentiation so well! This will help make sense of the whole task. Check it out!
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[@nayanpatel312]

It's sad to see that best videos of calculus on youtube are having such less views. Still you stand the BEST among the waste. Please, continue making more such videos & Thanks for making our studies enjoyable.

[@victorisrael6191]

People are not really interested in things like this but the people that really want to understand calculus value channels like this

[@nenzattibellece4459]

Some people are born to teach and this is a bless. You are one of those people, professor. So clear. Greetings from Brazil. I thank you for this video.

[@masthanyou]

Great sir. Thank you

[@ivan_ivan0v_]

Thank you!

[@607]

3:16 Wait, from what do we know that? It's not in the video that you referred to.

[@ddevil768]

If you’re referring to the quotient rule he covers how to use it here kzbin.info/www/bejne/l32UZoJsp7hssJIsi=Gkvaf0eAYJ2h9Yht

[@607]

No, I mean that tan(x) = sin(x) / cos(x).@@ddevil768

[@lucyla9947]

​@@607 that's basic Trig Identities. You should've learned that in Precalc.

[@607]

@@lucyla9947 Where is the precalc video?

[@aayushthapa9941]

Hey Jesus

[@evankvalvik9918]

I learned more from this video in 7:56 than I would reading my textbook for two hours. Excellent work!

[@technically6193]

than attending classes and paying thousands

[@thecompsciguy833]

@@technically6193 I'm just paying for the degree and syllabi, im using youtube for the actual tuition

[@drvir]

You have changed my life positively. You have enlightened me. I'm grateful

[@roberrplatt4214]

When it's time to check comprehension, I find myself doing samba around the room. This may affect my grade.

[@jakubpacua2351]

Another day of thanking god I found this channel

[@xenomorphbiologist-xx1214]

Dude u explained this so well. My professor just kinda glossed over and basically said “memorize these trigonometric derivatives.”

[@mranonymous_25]

When i my teacher taught me derivative of sinx, i just learnt it... today 3 years later i realized why... that illustration at 1:23 was amazing

[@FriendGd]

Not a math trained person: Anyone care to explain how does (cos x + cos^2 x + sin^2 x) becomes (1 + cos x) @ 7:16? Any material I can look up to?

[@ariannabuciol3954]

Hello! It's because cos^2 x + sen^2 x=1

[@ariannabuciol3954]

It's all well explained in the video n 88 of this same serie :)

[@Dcoooooooookkkkooo1]

I love earth

[@UnderstandPolitics]

POV: You're here for homework help (very generic comment)

[@fabiofabbianissillychannel9935]

Hey uep

[@ahmedjahenzaib148]

*Damn...this just gave me the whole conceptual picture of maths....YOU ARE THE BEST>>>>>.........Simple to the point and literally tells everything in a conceptual way*

[@sydv2005]

best professor in the world . was trying to understand this all for last one week . now almost all is clear just by watching 7 videos

[@aselim20.]

I wrote it.

[@RajeshSharma-tf2xx]

Dear Professor, Could we have a video to explain dirac delta functions, fourier series and fourier transformation

[@eggi_rius]

Try 3blue1brown

[@magiicbeans6405]

Realising that Cosine is just the first derivative of Sine kinda blew my mind, it makes a lot of sense with hindsight. Epic

[@tyfoodsforthought]

Ahhh, precisely the explanation I was looking for. Thank you!

[@cameronlight8504]

Loving your videos and I appreciate the depth of explanation on each subject.

[@livbensen1898]

literally binge watching these videos until my final next tuesday

[@maccathealpacca5853]

Nooo I have a maths test next week only problem, it's on integration. None the less still a useful video

[@ProfessorDaveExplains]

sorry integration is coming soon!

[@maccathealpacca5853]

Professor Dave Explains keep doing what your doing your content is some of the best educational wise material, it's clear and simple with neat little tricks that help get the information in

[@Dcoooooooookkkkooo1]

I love earth

[@inkspill3116]

Great visuals for both the graph and explanations! Very clear and easy to follow. Thanks for posting this.

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What's your iq? 195? By god you're amazing! Lots of love

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I knew Jesus Christ about 3 years ago and he changed my life

[@Kiky_MedPhysicist]

Thank you sir for your dedication and for making this free! 🙏

[@carolinehoak]

The fact this video was recommended to me the day we cover Trig derivatives in AP calc AB is amazing. Tank you professor Dave and the YT algorithm.

[@dhivyasree1141]

மிக்க நன்றி.வாழ்க பல்லாண்டு வாழ்க வளமுடன்.

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Jesus Christ is my lord and Savior and he can be yours too if you trust in him

[@samuelluan1593]

GREAT VIDEO thanks so much

[@MrSamGong]

very good explaination~!!!

[@adityashankar5267]

Prof, derivative of Sinh(x) is what?

[@ProfessorDaveExplains]

check out my tutorial on hyperbolic functions!

[@sitsokenzantetso1686]

Prof can you explain how when we derived sinx/(1+cosx) it expanded? P.S. sorry if its explained in your video my brain is just mush right now

[@duanedonaldson2262]

kzbin.info?search_query=sinx%2F(1%2Bcosx) so that I am not giving somebody else's direct video, there are different scenarios listed there.

[@abcdxx1059]

I was looking for this

[@ericfricke4512]

Bro.

[@afrobandit3911]

prof dave at 6:03 why did you divide cos X by one of the cos^2 X ? thank you for you tutorials.

[@lesserknownfacts7849]

due to the quotient rule

[@santoshgujar5237]

✨Thank you, Sir, 🙏🌺✨

[@potatomudkip]

Just realized im learning an 11th grade subject while I am 5th grade, a month away from 6th.....

[@bomaathuis7277]

I rewrote the derivative of x^2*sin(x) to sec(x)+x*tan(x)/cos(x) or is this too much. I was just wondering hence you said there isn’t much we can do after the answer (cos(x)+x*sin(x))/cos(x).

[@carultch]

There's plenty you can do after the form he gave, just not much you can really do to make a simpler expression.

[@egggames8059]

@@carultchI mean whenever u can get rid of a denominator u do, no?

[@carultch]

@@egggames8059 I suppose, yes. You might also have a goal of keeping it only in terms of standard calculator trig functions, rather than secants, cosecants, and cotangents.

[@tGoldenPhoenix]

Done.

[@amanshukla6694]

Much thanks to you

[@ibissantananavarro7586]

Thanks

[@yosephTiruneh]

Great go on

[@viviandelossantos6085]

Thank you very much!

[@duanedonaldson2262]

For the elementary functions, memorize the Magic Hexagon and utilize it for elementary calculus

[@snehageorge4853]

Thank you so, so much for this short but sweet video on proving trig derivatives visually. I have terrible memory, and couldn't come to just memorizing them without truly understanding. this video helped me a lot. thank you infinitely ♥

[@streamungodlyhour676]

same

[@davidmajor1508]

This video doesn't "prove" a damn thing. All it does is visually illustrate. Typical of "Prof Dave" he vastly oversimplifies and therefore ultimately misleads.

[@carultch]

@@davidmajor1508 He's not claiming to prove anything in this video, nor is he giving an oversimplification that would give misleading ideas. He's just giving idea behind how you can intuitively understand the derivative cycle of sine and cosine, and how you can recall it quickly, if you ever forget. Most people who will use practical applications of trigonometric derivatives don't need to know the formal the proof through the squeeze theorem from first principles, but knowing this illustration can help you recreate what you really would need to know.

[@davidmajor1508]

@Carl Hansen The person I responded to DID indeed mention "proof". READ.

[@davidmajor1508]

@Carl Hansen How does this magically help one "intuitively" understand?

[@TomatoExpress24]

can anyone tell me that when we multipy why dont we direct find derivative and then multiply

[@TheLethalDomain]

Because when you are only interested in multiplying numbers together, you're not really interested in finding the difference of something along a curve. You're solving for an exact value. This is why calculus is separate from other fields of mathematics, though many higher fields of math and physics rely upon calculus when studying systems that change over time.

[@607]

4:00 Can't you let the cos2x's cancel each other out, and end up with sin2x/cos2x?

[@ddevil768]

No you can’t, because the entirety of cos2x + sin2x is being divided by cos2x. Kinda like if you did (1 + 3) / 3 you can’t just cancel the three’s. If you separate everything you could get 1/3 + 3/3 so if you did a similar thing with this example problem you could get cos2x / cos2x + sin2x / cos2x which simplifies to 1 + sin2x / cos2x which is the same as 1 + tan2x. And according to the pythagorean identities 1 + tan2x = sec2x which is the exact same answer he has.

[@607]

Thanks! I wonder if I'm going to need to memorise all these identities.@@ddevil768

[@thecompsciguy833]

YES!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

[@anthonystark6215]

Thank you, Professor!

[@neuronoc.7343]

You are a literal godsend.

[@abdullahbarish8204]

Amazing

[@kamogelomathabathe9761]

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[@Attalla-t9b]

I guess trigonometry in calculus & post-calculus is really just about memorizing 🥲Takes too much time to derive them one by one.

[@AkbarAli-lc7vy]