I'm older - middle-aged and the way I learned we were taught to use a delta x instead of h, but no worries I understood every step because you've got a KNACK for teaching. Thank you, sir, whoever you are.
I have done very, very well in my exams, just following your videos, although I do not have to learn the proofs, it gives me a much better understanding of what's going on, so it's fundamental to learn this.
T/y/v/m for this mathematical explanation of why the derivative of sinx is cosx. I've seen a YT defining it graphically but still can't absorb that method; this one tho does :make sense. And hopeful it will now ease along "seeing" the graphical proof. T/y again.
Can you explain how we turn the limit of X+ H into the angle addition formula when proving the derivative of cosine = - sine and sine = cosine? I find the formula for Sum to Product easier to use as it makes more sense when say cosine - cosine and we use the Sum to Product formula
Shaun Kirk the video explains how we do that. Did you have a specific question on one of the steps? The sum to product formula applied to sin(x+h) - sin(x) and same for cosine also works and may even be a bit simpler. Didn't occur to me at the time because it's a less commonly used family of formulas in my experience.
Could you please link to the video where you actually proove that the limit as x goes to zero of (1-cosx)/x equals zero? It's easy if you use the Taylor series of cos(x). But what, if you start from the scratch?
It's the limits that are equal, not the expressions inside the limits. limit as h goes to 0 of [(1 - cos h)/h] = 0 limit as h goes to 0 of [(cos h - 1)/h] = 0
You could also have said that since h -> 0 and cos(0) = 1 the (cos(h)-1)/h would be 0/h = 0, no multiplying 0 with -1 needed :-) (This was at the end of your proof for sin' )
Thomas Efternavn no, you can’t do that. If you let h go to 0 in the numerator then you have to do it in the denominator also. And that would give you 0/0 here, which means something else needs to be done.
I'm older - middle-aged and the way I learned we were taught to use a delta x instead of h, but no worries I understood every step because you've got a KNACK for teaching. Thank you, sir, whoever you are.
Thank you! Finally someone who explains it properly.
You explain very nicely in an easy way, sir!
I really liked your video, I could understand the topic very easily...
Thank you...😊✌
I have done very, very well in my exams, just following your videos, although I do not have to learn the proofs, it gives me a much better understanding of what's going on, so it's fundamental to learn this.
personally i can't bring myself just to memorize formulas without understanding why they work
coffeebirdtree same bro same
Best teacher ever ,God bless you
Sir i am from india but sir you teach so much better than indian youtube teaching channels
This is beautiful! I hate when we are given formulas without telling how they arrive. Thank you! I study math on my own for hobby.
i think you should lecture my lecturer...
Fantastic video mate :) Thank you for showing this so clearly, and for taking the time to do both :)
After all i found it thank u very very much this was an incresible piece of work
O how i wish i could personally thank you sir.. Thank you for this most informative proving for the derivative of sin x and cos x
U made it much simpler 🙌🙌
sir very satisfactory explanation thank you
thank you for this. really helpful.
I would have gotten an A in Calculus 1 if this lecture (and TH-cam) was available back in my day (I took Calculus 1 in 1989)
Thank you for your help !!! I finally could finish my homework !!!! thanks :)
T/y/v/m for this mathematical explanation of why the derivative of sinx is cosx.
I've seen a YT defining it graphically but still can't absorb that method; this one tho does :make sense. And hopeful it will now ease along "seeing" the graphical proof. T/y again.
u r the undisputed champion
Your the great master keep it up
Thank you sir for this explanation
Thanks for helping us with providing of this video .
YOU JUST SAVED MY LIFE
Awesome video
How i get derivatives of complex trigonometric equation
Can you explain how we turn the limit of X+ H into the angle addition formula when proving the derivative of cosine = - sine and sine = cosine? I find the formula for Sum to Product easier to use as it makes more sense when say cosine - cosine and we use the Sum to Product formula
Shaun Kirk the video explains how we do that. Did you have a specific question on one of the steps? The sum to product formula applied to sin(x+h) - sin(x) and same for cosine also works and may even be a bit simpler. Didn't occur to me at the time because it's a less commonly used family of formulas in my experience.
14:10 how is sinh/h=1?????
It's not. The limit of that as h goes to 0 is 1. I have a video that explains that, called "special trig limits proof 1"
@@TheInfiniteLooper K thanks I'll check it out
Did you learn all of this from your professors at UPenn? Or did you have to study on your own?
This was all before Penn. I finished Calc 3 before going there.
Could you please link to the video where you actually proove that the limit as x goes to zero of (1-cosx)/x equals zero?
It's easy if you use the Taylor series of cos(x). But what, if you start from the scratch?
th-cam.com/video/NXWXEd78lsM/w-d-xo.html
Thank you very much!
thank you my best techaer
very helpful man. thanks
you are amazing !!!!!!
thanks verrrrrrrry much...ts all clear now!!!
link to the proof of the limits would be helpful
This is a very good video. I have the proofs here. th-cam.com/video/64dguvQBwUQ/w-d-xo.html
And from that basis, you can get the derivatives of the other 4 expressions (tanx, cscx, secx, and cotx)
Thank you
Thank you very much
plz tell me how cosh-1/h =0
because 0/0 is not zero
I have a separate video explaining why that limit is zero. Search special trig limits on my channel, it should be one of the first few results.
Your numerator is missing grouping symbols.
Thanks a lot .... .
Thanks
THANK YOU
Math is fucking beautiful.
Stop your major cursing. It is ignorant and needless, especially on a mathematics forum.
Sir tan function ka proof please😫🙏🙏💓😫🙏🙏💓🙏🙏🙏
d/dx(cosx)
=d/dx(sin(pi/2-x)
Use chain rule and you will get
=-(cos(pi/2-x))
=-sinx
It would be better if you explained it with the help of Graph
How does (cosh-1)/h equal (1-cosh)/h? Wouldn't it be equal to (-1+cosh)/h instead?
It's the limits that are equal, not the expressions inside the limits.
limit as h goes to 0 of [(1 - cos h)/h] = 0
limit as h goes to 0 of [(cos h - 1)/h] = 0
Can you be my teacher
You could also have said that since h -> 0 and cos(0) = 1 the (cos(h)-1)/h would be 0/h = 0, no multiplying 0 with -1 needed :-) (This was at the end of your proof for sin' )
Thomas Efternavn no, you can’t do that. If you let h go to 0 in the numerator then you have to do it in the denominator also. And that would give you 0/0 here, which means something else needs to be done.