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

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

[@jan-willemreens9010]

...Good day to you Newton, I hope your well deserved rest has done you good. What I like about your presentations is that you give the interested viewer the feeling/impression that a mathematical journey of discovery is being undertaken together; it doesn't all have to be perfect, at least that's just my opinion, as long as the core of your message is reached. As an officially non-mathematician (math hobbyist I call myself) I am still very enthusiastic about this branch of bèta-sciences, especially because of these kinds of surprisingly subtle derivations. Finally, I have just a short comment to make at about time 9:09, where instead of 0 times 1/sin(x + h), it should be 0 times 1/sin(x), after all you also have to take the limit of 1/sin(x + h) for h-->0, according to the official rules (limit multiplication) of course. It was nice to see you back in action again! Now we as viewers can fully go on with our academic lives together with "Sir" Newton as the captain (lol)... Thank you Newton, and only the best to you, Jan-W

[@PrimeNewtons]

Thank you , Jan-W. I hope to keep going for a while again. I noticed the mistake too. I just wanted to move on. Lol. Your feedback is always precious.

[@jan-willemreens9010]

@@PrimeNewtons ...I have just 2 spicy limits for you: Limit #1) lim(x-->4)((sqrt(x + 5) - 3)/(x - 4)), and Limit #2) lim(x-->7)((2 - sqrt(x - 3))/(x^2 - 49)). If you find the time, try to solve these limits without applying the "boring" conjugate method, good luck Newton...

[@PrimeNewtons]

I used my method and found #1 as 1/6 and #2 as -1/56. My second attempt is to use your suggested method. I am curious to see how much easier or harder it would be.

[@jan-willemreens9010]

@@PrimeNewtons ...Newton, I got these two limits from my old math school notebooks, which was a time when I was experimenting with limits in general while doing my homework. Don't immediately think I was such a learning freak, on the contrary, I was more on the sports fields (lol). I now give voluntary math tutoring from time to time to neighborhood youth who sometimes need a helping hand. A very satisfying occupation, I think this suits me better than real teaching; you have much more direct contact with these children. Let me know Newton, if you managed to solve the limits applying the so-called "Jan " method, according to none existing textbooks (lol). Otherwise I will send you my solutions. I found the second limit quite interesting, because of unexpected turns during my trial and error process. The answers you gave are correct, at least this is a good starting point. Thank you Newton in advance for your sporting participation. I maybe have an interesting suggestion for you for a presentation in the future, just to show the interested viewer that there are more creative paths to the same outcomes of these problems; often quicker and more effective, instead of conjugating or using the Hospital (lol)... Jan-W

[@vincentmwandiki5098]

My brother Newtown you are the legend in my life... thanks 👍👍👍 may God bless you

[@jasonmarshall6320]

You are an amazing teacher, thank you for your videos

[@user-ms5cm4ok4h]

Sir watching you from India 🇮🇳

[@user-mj6rr1xn3t]

Gracias Bro, acabó de descubrir un tesoro con tus vídeos.

[@refilwemekgwe6527]

From RSA♥️🤗thank you

[@lincolninniss5781]

Good afternoon. Another approach is to write the difference sinx-sin(x+h)=2cos(x+h/2)sin(-h/2) by the factor formulae.

[@punditgi]

Nice series!

[@user-id5do9ly3z]

Good serie of videos

[@abdoulie1027]

Thanks for the video ❤

[@miguelschainlife3520]

I love you sir thank you so much 😂

[@cardi05]

Please help with Chain Rule

[@KanoShampene-wi4qt]

Please help with the derivative of x^(1/100) from first principle

[@PrimeNewtons]

Next video

[@KanoShampene-wi4qt]

@@PrimeNewtons thanks