Calculus 1 Lecture 2.5: Finding Derivatives of Trigonometric Functions

[@AP-pm9qy]

Right now its 3 am on a Saturday and I'm staying up to watch Professor Leonard's calc vids. I told myself just one more and here I am. As someone who spends their time on Netflix and suffers from chronic laziness, Professor Leonard managed to engage me so much so that I'm binge watching his videos and taking notes like its a new and hot Netflix series that came out. You sir are legendary.

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These videos should be on netflix

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@@dougjohnson5487 I now am late but the prof now has a precalc section in which he covers trignometry extensively.

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You are a very mindful professor. My professor will make anybody feel like they're stupid for asking any question about algebra.

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After all these years, I have found the perfect video series. It's 6:43 am, I stayed up all night studying for an exam today (probably a bad idea), and just found these videos, and now I can only be jealous that I dont have a professor this good at teaching. Hopefully watching these lessons will save me today

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did it save you ?

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@@jash8281 I dont remember about that specific exam, but I passed the class with a C so I'd say yeah it did enough

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If it’s not a secret: what university?…

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@@mary56789 Northern Arizona University

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How'd it go?! Are you in calc III now?

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@@freezinginhere He got me an A in Calc 1! I definitely don't love math the way he does, but his lectures made it make so much more sense. I didn't even bother watching my own instructor's videos once I found this channel.

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@@absentvictim My instructor doesn't even have videos, he just posts links to Professor Leonard and The Organic Chemistry Tutor and then gives us a bunch of homework. I'm so glad I'm paying for his services -.- I wish the money went to these youtubers, since they're the ones doing all the work for my education.

[@absentvictim]

@@voxvolhynia5400 I agree completely!!

[@roblox21242]

@@voxvolhynia5400 my instruction is the same, these people should be fired they dont even try, instead uses someone's work as their own. and i looked up how much my professor makes, he makes roughly $120k a year and does nothing. imagine that.

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I wish my tuition money was going to you instead of my half-assing prof at UTA

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arlington in da house!

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Felt this in my soul 💔

[@stevensteezy8420]

9 years later and UTA still got those type of professors

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@@stevensteezy8420 lmao that is hilarious. My god this vid gives me PTSD just thinking about those times. Good luck man.

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9 years later. is it worth it?

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[@brianwahome2897]

I took a weekend break when you said: "We will get to the rest of it next time" at 3:53... Excellent work Prof.

[@UndoneJigsaw]

I am preparing for my Calc class for spring 2019 with my former trig teacher in spring of 2016. I earned an A in trigonometry in her class. I got a B in Precalculus with a teacher that talked really fast. I had to take a 2 year break from school in 2017 due to life struggles but during those two years I have been watching math videos and looking over my notes. I am going to do whatever it takes to understand Calculus so I can go on towards Calc 2 and Calc 3 and Professor Leonard's videos has helped so much in understanding Math, thank you. I also noticed a pattern in the derivatives of trig functions. Every trig function that starts with a "C" (Cos, CSC, COT), the derivative is going to be a negative. Pair TAN with SEC and COT with CSC.

[@quanesshatheseventeenth8617]

Aye did you succeed bro?

[@UndoneJigsaw]

@@quanesshatheseventeenth8617 yes. I received a high A in Calculus 1, Calculus 2 and Calculus 3. I have to say thank you to professor Leonard's videos as well as taking a good instructor that was a visual learner like me. Now I have been tutoring those classes for the past 3 years.

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wow man thats awsome@@UndoneJigsaw

[@rwharrington87]

This is fascinating after taking your Precalculus/Trigonometry course. Knowing how you can use sin and cos to model oscillations and now being able to obtain the rate of change at a given time is really enlightening. I tried going through this course several years ago, and this lecture was so perplexing at the time, not knowing the prerequisites, that I gave up. Now 4 years later it seems really easy. Filling in that missing puzzle piece in your course list was clutch sir, and needed for so many of us.

[@dudestaytuned4542]

I used to cry out of frustration during my first semester calculus, thank god I found this channel. Not only helped me understand but also helped my mental health. Now calc is kinda fun haha

[@scenario1741]

I wish my calculus instructor taught as well as you do. This is saving my future career. THANK YOU!

[@a.robberts4225]

2021...and this channel is still my favourite.

[@magdielissuarez7837]

This guy makes me love math again!!!!!! THANK YOU

[@Peter_1986]

"Make math great again!"

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I wish my calculus teacher was like you , if there is someone who's making me feel like calculus is fun to learn then it is surely you , Prof Leonard , thank you so much for all your videos.

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For all students who visit this guy's KZbin channel"this guy deserves way more"(thanks prof for being a cool teacher I admire you...we all are lucky to find you ..)and I know I am not the only one whose complete perspective of calculus changes within one playslist You will forever be my favourite teacher❤️ Thank you my real life superman🙌 Ps(yeah I know he don't check comments)

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How a great explanation! Good job professor 🤓 .. your new student from Saudi Arabia 🇸🇦

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🇸🇦🇸🇦🇸🇦

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God bless you sir, i have learnt all of my calculus from your videos so far.

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"Good deal, alright!" Haha cheers mate, your classes are brilliant, you are the reason I'll be passing calculus this year!

[@aliozcol850]

Sir, from your previous lectures finally I've learned how to easily prove if a mathematical expression is true or not. Thank you for your work. I'm proud to say I can finally prove derivatives of trigonometric functions by myself without asking someone.

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Can you also do workout routine??? Lol hahaha

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Thanks so much! I have watched many videos, but I find yours are always the best!! I'm taking calculus right now in the spring semester and was getting lost with my professor.... you're saving my semester!! you explain the concept really well.

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Ok I seriously need to have him as my new teacher. He has helped me to decipher Calc and help me complete my goal of completing Calc 1 by 16 years old. This is much appreciated. You have my many thanks.

[@LC-wv7tz]

Thanks for making these, like all the others have said and will continue to do. I'm a somewhat older student coming to university for the first time. At the recommendation of my college I went through a precalculus and calculus I sequence that for some reason included NO trigonometry. I didn't realize what I was getting into at the time or what I was missing out on, but I've since transferred to a new university and into a calculus II class (somehow my calc I class transferred despite the curriculum covering NO trig) and am scrambling to catch up in some ways. Of course I'm ahead in others as my old school Calculus I course covered almost all the topics concerning integration and The Fundamental Theorem normally covered in calculus II. I did take trigonometry in high school, but that was a while back. These lectures are rather helpful. All I really need is to get my hands on a good trig handbook now to cover those fundamental parts.

[@greense65]

You will generally find trigonometry covered well in just a few chapters of a precalculus book. I recommend Algebra Structure and Method by Dolciani and Brown or Advanced Mathematics by Brown. These books are written in a lean style, but given that you have done some coursework beyond this level, you should be able to handle it and will benefit in your future math by getting comfortable with this style of writing. The exercises are well-chosen. If you can do the A and B level ones, you will be fine for calculus, but I recommend working on the hard C level exercises, too, because, as I said, they are well-chosen. Dolciani also wrote Modern Advanced Analysis, also written in a lean style, which has chapters on trigonometry (and even has some other chapters introducing calculus). All these books are long out of print, but are available used at reasonable prices. I carefully worked through the first two of these books, in the order listed, and they have been a huge help. Another choice is Larson's Precalculus. This is a book still in popular use, although I would save a couple bucks and not buy the very latest edition.

[@LC-wv7tz]

Thank you. I appreciate the recommendations for textbooks and I will check them out. I was surprised, when I tried to consult my professors on this topic I was met with just some shock, they didn't have much to say on the topic of recommended texts, so I figured I'd turn to sources like this or MIT Open Courseware to do some self-study. I'm actually in school for physics and mathematics, so I will be using trig quite often and I don't feel intimidated by sitting down to read a math text. Those sound just like I was looking for.

[@greense65]

Based on your reply, I am even more comfortable recommending the Algebra Structure and Method Book II (I should have added the book II part above; there is a book I, which is first year algebra-too easy for you, and no trig) or Advanced Mathematics book to you for the trig (and precalculus in general). You seem to have more than enough mathematical maturity to handle their style, and will actually benefit from getting used to it. For other people reading this chain: In general, since you are on a calculus video website, you are most likely able to benefit from these old Brown and Dolciani books as a good precalculus reference and source for brushing up. These books can be a little tough for those intimidated by math and who don't have a good teacher. My personal story with them is that I had the Algebra I book way, way back in time (in the 8th grade). My teacher wasn't good, my parents didn't know enough math to help, and I was a pretty lazy student, so it didn't work out for me, and I actually blamed the books a lot (unfairly, instead of blaming myself-although I did blame my teacher, too, and he deserved it). As an adult, I came back to the series and really appreciated it. The writing style is an austere math writing style and there aren't tons of worked examples. But the exercise sets take you carefully from easy to pretty hard. There are solutions manuals available for sale, but in contrast to the low price of these old, used books, they are expensive.

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coming back after 10 years

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[@luciusirving5926]

Derivatives are awesome, easier than electromagnetism in physics. I could never do Coulomb's Law or any of those formulas related to electromagnetism like I do derivatives. Non-Newtonian physics is even more complex than linear algebra.

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that explanation at 37:25 clarified a lot... thank you... I love when questions I needed to ask that I couldn't think of are asked and answered

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38:00 I am glad the student asked that question. I was thinking of that same exact thing myself throughout the video as well.

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38:15 The student actually had a good question... the professor's explanation helped me finally understand why d/dx(sin(x)) is cos(x). I feel so enlightened....

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Nilmini Deen, Applying the derivative formula for inverse sine and using the product rule for differentiating the inside function 1/x, whose derivative is -1/x^2 d/dx [arcsin(1/x)] = -1/sqrt(1-1/x^2)x^2

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Not fing joking. 18:02. I am watching this stuff because during covid I passed and now I am having trouble in Physics.

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11:02 "Isn't that interesting?!" "...no" "No? No. Don't care.............. You're gonna care" This guy is a savage to his students sometimes hahaha

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Youre better than any calculus professor at UCLA lol tysm

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By the way, apart from lectures of the professor, I also like the laughter of one of the students :)

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ive watched so many of these that I know who you're talking about - Scotty i think! the professor talks to him during these videos sometimes LOL

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I feel like I am going through hyperspace going through a few of these videos.

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This makes me miss my math classes :(

[@melissap6666]

As a note: There's a mistake at the beginning: It should read limit of x approaches 0, not h. For sin(x)/x and (1-cos(x))/x. Later the usage of h is correct. After the break both expressions are corrected.

[@cornelxbox25]

No. It's as h->0 because it comes from the difference quotient (much earlier chapter).

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God bless you sir

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Thanks our HERO!

[@nicocapa123]

Wow 37:30 made me finally understand.

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Bthis was fun to watch

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Wish you were my teacher

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Thank you great professor

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Damn, Prof Leonard is buff!

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Could you please turn on captions for this video?

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thank you so much for these videos

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Thank you for this!

[@TheFarmanimalfriend]

I have an eternal problem with sin(h)/h =1 as h -> 0. I can use L'hopital's rule when limits become 0/0 then sin(0)/0 evaluates to cos(0)/1 which is 1.

[@alondraherrera4170]

why is this mans so ripped

[@monicavictoria5818]

You and NancyPi are my favorites and I probably won't survive calculus without you both, btw, you guys would make a cute couple

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I wish I could of had you as a professor. Thank you sooo much for uploading these videos!

[@thefacelessmusician1145]

In the word problem would you get just -sin(X) instead of 3sin(X)? given that the derivative of -3 is 0

[@sarahransomm]

Outstanding, thank you.

[@khalidbornaparte6250]

Thank you professor

[@elliotsmythe9098]

Why do the derivatives of trig functions cycle through themselves every fourth iteration in the same way that the power of i cycles through itself every fourth iteration?

[@filmonhaile3327]

at 33:00 I think it can go further to 1+ SEC(X)

[@kai-shanetblackwood7166]

You are saving my life.. >.

[@TheFarmanimalfriend]

I am having a problem with sin(h)/h and cos(h)/h as h -> 0. It seems you are dividing by zero. Can you direct me to where that proof is explained better? I am missing something. Maybe there is a textbook that explains it better? I have already taken all the Calculus classes and am going over all my classes. Calculus is, by far, the most interesting subject I have ever taken and I'm wanting to understand stuff I glossed over before.

[@akangkshyadutta2581]

kzbin.info/www/bejne/jITUgI2EirGFoLM Check it

[@JackTheGamingGuy4REALZ]

Sorry this is late, but if you've seen the earlier videos, the limit as h->0 doesn't mean h = 0, because then why use limits? We use limits to say what happens as h gets arbitrarily close to being 0, while still avoiding the domain issue. It's really a neat trick

[@JoRdaNianCR7]

good job prof

[@sharanjaiswal6983]

I have one doubt at time 32:45 . Since 'x' is variable, and cos(x) could possibly be -1 somewhere, therefore 1+cos(x) could be 0 somewhere. Then, how did we cancel this expression [1+cos(x)] from numerator and denominator?

[@rapslikeaprva]

at that of x=(2n+1)pi point the function y wouldn’t exist .. so we wouldn’t be taking the derivative in the first place .. if we are taking the the derivative of a function it means that it should exist .. and so cosx is not -1.. and hence can be cancelled

[@abdulwahabraheemi]

you are the beast

[@zeyism3981]

Thank you Prof !!!! 💪

[@allanchen6170]

i remember it like sin is - mean sin and csc. and tan is sec and cot is -csc

[@kizarumelon2477]

actually useful lol good job

[@rudnam]

enjoyable thank you

[@kal5211]

Thanks again!