Derivative of tan(x) from first principles (definition)

In this video I showed how to use the definition of the derivative to find the deriative of tan(x)

[@SIERRATREES]

I am retired and just started doing maths again. I find it fascinating and endless, and very satisfying when mastery is gained ; its also good distraction from this turbulent world, like a meditation. This work by Newton is clear and extremely helpful.

[@chiagozieazodo3604]

I Love these Tutorials So Much, Prime Newtons just has to be the BEST Math KZbin Channel I have ever come across. NEVER STOP LEARNING. Thank you so much Prime Newtons❤️❤️❤️🙏🙏🙏🙏💯💯💯

[@jan-willemreens9010]

...Good day Newton, These kinds of proofs make mathematics personally so much fun to study. Great presentation, and I just wanted to pass on to you that I learned that the procedure is called "First PrincipleS" with an "S"... Thank you and take care, Jan-W

[@PrimeNewtons]

That is correct. Thank you for your keenness. Now I have many titles to fix 😄

[@johnnolen8338]

There is another way to prove this from first principles. Your approach is much simpler and quicker but the difference quotient: [tan(x+h) - tan(x)]/h can be expressed as [tan(h)(1 + tan^2(x))/(h(1-tan(h)tan(x)))]. Taking the limit of this expression as h tends toward 0 yields 1 + tan^2(x), which is the Pythagorean identity for sec^2(x) ◼

[@jumpman8282]

Yes, using the angle sum identity for tangent is super straight-forward. Just put the terms in the numerator on the same denominator and the whole thing basically solves itself! The only thing we need to realize is that tan(ℎ) ∕ ℎ = sin(ℎ) ∕ ℎ⋅1 ∕ cos(ℎ) which then clearly approaches 1 as ℎ approaches 0.

[@econhelp583]

Great presentation! It was very clear and helpful. I also liked the last piece of advice. I agree 100% about the pursuit of learning. I strive to be a life-long learner. I am still studying at the age of 58 (taking a math class at my local university). My first four degrees were fun (BA,MA,MS,PhD) and my job is great, but learning new things every day is what really keeps me going. Thanks for this video, it was awesome to watch!

[@PrimeNewtons]

Wow! Tou are an inspiration.

[@econhelp583]

@@PrimeNewtonsThanks! I give the credit to family who instilled in me the value of education. Both of my grandfathers were from immigrant families arriving in the USA around 1905. My Swedish grandfather’s family immigrated to northern Minnesota and it was a hard life there. But my Minnesota grandfather worked at an ice cream factory in Minneapolis to help pay for his education at the University of Minnesota. He kept on getting degrees. He got a DVM and then a PhD in microbiology. As he was finishing his PhD, he was drafted to serve in WW II. Because he was older, and because of his education, the U.S. army decided to make him a captain even though he had no military experience. He was in Italy for years during WW II, and that was hard because he had to leave behind my grandmother and father. War is a nightmare, but he was lucky to get through it to return home. After the war he was offered many university positions but he decided on being a research scientist at the Mayo Clinic instead. Education brought my grandfather from being a poor immigrant who had to wear shoes that were falling apart to a life later on that he enjoyed. He was a great role model. The world needs great role models (teachers) to help the next generation live happy and well thought-out lives.

[@PrimeNewtons]

That is a blessing!

[@MyOneFiftiethOfADollar]

Thanks for the update on all the degrees perched on your mantle. Did your parents help you financially while earning those degrees?

[@kenlance]

My mentor ❤🎉 Mr Prime ... you changed 60% of the students who had negative attitude toward maths...here in kenya 🇰🇪 😅😅😅 you will not remain the same Mr prime 🎉God blessed you🫡🫡🫡🫡

[@lyricaltherapist2994]

Coming to watch your videos at the end of the day makes feel like a genius in math.. Thank you

[@whodhoni]

the way my man explained was damn good, from India ❤

[@yplayergames7934]

It's 10 pm in Brazil and I just thought: "How is the derivative of Tan x by the first principle, and then I found this guy one of my favorites math YT channels" Thanks Prime... this video couldn't be clearer than it aleeady is, nice job

[@crishzZ]

Thankyou sir ✨️ Love from KERALA India❤️

[@martinpmaniputhenpurackal]

Excellent I too follow him, from Kerala

[@MyOneFiftiethOfADollar]

Nice Job. More typical is the mindless quotient rule which a lot of us could not prove from "first principles".

[@henryfayol6667]

U are such a genius tutor

[@punditgi]

Many thanks for these videos! Good to know these derivations!

[@holyshit922]

I used formula for tan(x+y) and had to taclulate limit limit(tan(h)/h,h=0) Finally I have got following answer (tan(x))' = 1+tan^2(x) and in my opinion this form of answer is more useful especially for integrals

[@PrimeNewtons]

That's impressive!

[@ianmyers1190]

Such clear and concise tutorials. Awesome job thanks,

[@Kibo-sama]

Love from India sir , you're an amazing teacher

[@PrimeNewtons]

All my love 💓 ❤️

[@inayatali3953]

From Pakistan ❤

[@Tshitego]

Thank you sir love from Botswana

[@constancephilip_]

Thank you so much! You make learning easy! 🤗

[@meriamsuyom3175]

Keep posting im from the philippines you explained well God bless

[@MaatlaTlhalerwa-m4k]

Wow 🎉❤......understood very well 🎉❤

[@TendoJemimah-z9o]

Nice teaching

[@adamabemmah4382]

This is great 🎉

[@ahmedhafez5648]

Amazing 🤩

[@its_me_zryz]

New subscriber💥 . . . . Thankuhh sir❣️

[@emmanuelonyango9497]

Thumbs up man....

[@misheckmwendalubi9480]

We love it 💖

[@nope5735]

understandable, thank you very much teach

[@RubenRuben-zj6qz]

Your video are good can you please do more of intergration of tanx cosx sinx please😊

[@cedengwabengz7922]

Thank you.

[@othmanabdalamohamedadanabd1978]

Good

[@snowman2395]

i dont understand how he went from sin(h) / h to 1 ... if h is going to 0 shouldn't that be 0/0 indeterminate?

[@CorneriousChilufya]

make a video for a derivative of ln

[@said14121]

رائع

[@said14121]

❤❤❤❤

[@maxstirner42]

Is it possible to solve it without using sin/cos?

[@PrimeNewtons]

I've never tried it. Nothing is impossible

[@olayiwolafatimah2976]

😇

[@davidbrisbane7206]

Hmm... I could say, "Don't start learning, because those who did all died!"

[@ajikeruth2789]

There is a mistake man 😢