In this video, I showed how to find the derivative of sin(4x) from first principles. This process involves the use of the angle sum identity and other limit identities in relation to sine and cosine as the argument approaches zero.
Resources like this didn’t exist when I took calculus back in the mid 1980s. My background is astronomy and physics and after teaching them for 30 years, I found students too often just memorized shortcuts for derivatives and couldn’t explain where the shortcuts came from. The notion of going back to first principles resonates with the kind of reasoning physics courses should impart. After all, there’s only one “rule” to remember, and while it may sometimes be difficult to apply analytically it can ALWAYS be applied computationally. Your channel is pure gold! Thank you.
So did I and I also learned calculus at about the same time. When I did my military sevice in Sweden, the library had the CRC handbook which felt like a goldmine. I found so many good things that I didn’t know about. I learned about first principles of course but I don’t remember we had them in tests.
Thanks for this very informative video sir, I've successfully differentiated sin2x thanks to you! Just a small thing i noticed: when you divide (cos2h-1)/2h and multiply by 2 as well to make no change, you shd also indicate that when lim h --> 0 , lim 2h --> 0 as well ryt?
I think it’s really good to show how these derivates are actually calculated. I don’t remember that we had to do this when I learned calculus. Most just look it up in a formula book. I have a good one that I bought when I had left university. Sadly, it doesn’t show how you actually get to the final result.
You dont need to memorize limit limit((cos(theta)-1)/theta,theta = 0) because it can be easily reduced to the limit limit(sin(theta)/theta,theta=0) for example by double angle identity for cosine and Pythagorean identity
What a Genius ❤🔥🔥...Thanks a lot sir i was trying to solve this question, but this seems to be one of craziest question to me and you just solved it thanks alot sir ❤️❤️❤️
Thank you Sir. It will be good, if you will leave the board for 2-3 seconds at the end of the video, in order to pause and review all one more time. Thank you
...A good day to you Newton, I hope you're doing well. A brief message from me. It's a busy preparation period again for the finals in may 2023, which for me means plenty of voluntary tutoring, and therefore a little less communication with you via your channel! Still follow your presentations regularly though, and this again excellent one I can use very soon for explaining/finding the derivative of a function by applying " First Principles " ... Thank you Newton and stay well, Jan-W
