Derivative of sin(x) and cos(x), PROOF 

"sine and cosine are like homies" #yay

I saw a student using L'Hospital for this, it made me really angry because he used sin'(x) to calculate sin'(x)

Prefect! I didn't know that cosine stands for complement of sine. Thanks for the video!

Can u do that proof of cosh-1/h and sinh/h

Student: I'm so smart, I know how to derive all the trig function derivatives Bprp: Really? Can you show me it for sin and cos then Student: ... #yay

You can also use the identity sin^2 + cos^2 = 1 and derive both sides then you got (sin^2 + cos^2) ‘ = 0 and (cos^2) ‘ = -(sin^2)’ so 2cos*(cos)’ = -2sincos and so (cos)’ = -sin

I ended with lim as h->0 cos(x)*sin(h/2)/(h/2). Using some tricks with the e^iz formula xD.

Master Cao, no explanation of why (cos(h)-1)/h tend to 0 when h tend to 0

In summary, It's like 19÷4 = 19/4

Thanks a lot sir . Amazing explaintion 😀

God bless you instead lecture was superb 👏🏻👏🏻

Nice! I hadn't thought about using complementary identity to prove the derivative of cos(x)

Why not do the derivative based on the Maclaurin series for since and cosine? The approach you used here has the issue that, without the numerical ✋ waving you might have been stuck with L'Hospital's rule, essentially needing to know the answer to the derivative you were trying to find. Maybe there's a non-circular, rigorous way to solve the "0/0" limits without L'Hospital's rule, but it didn't come readily to mind.

Can you prove tan(x+y) = [tan(x)+tan(y)]/[1-tan(x)tan(y)]? BTW thanks so much, I learned much in your videos.

I am not an adult I'm 12

I understand good 😊😊😋😋

Best teacher in world ❤

saving lives in 2022 T-T thank you for this

Finally, a video that I can understand xD

2:05 for those ho want to understand how he get the rule; go watch videos about addition and soustraction for cosinus and sinus cos(a+b) cos(a-b) sinus (a+b) sinus (a-b) it s kinda difficult but you will understand it ; then after that get back to the video

I wonder where trig identities come from, would you please explain us? Thanks :) #yay

Since we're all adults now... Tee-hee! 😁

how to proof the lim for (cost(h)-1)/h is 0? 0/0=infinite

I figured out two proofs that don’t use the limit of sin x/x, the limit of (cos x-1)/x, or any angle-sum identity. One uses the definition of arc length (as well as the Pythagorean theorem, the fundamental theorem of calculus, and the derivative of sqrt(1-x^2)), but the other one just uses the parametric definition of a derivative (d[x,y]/dt=[dx/dt,dy/dt]). If I ever teach a math class, I will be looking for one of those.

can you use the definition of the derivative for e^x??

the doraemon theme playing at the start is just awesome

Hey brother could you please provide a geometrical proof ?(actually, I was anticipating for one such proof........ )

It is nice Thank you so much

You are my Best 👌 👍 😍

The limit of (f(x+h) - f(x)) /h Where did it come from??

This is really neat! Glad I found this! =D

Why write cos(h) please tell me sir 1:59 video please explain Sir

A more elegant and compact proof exists which uses the identity SinC - SinD = 2Sin(C-D)/2*Cos(C+D)/2 together with the limit Sinh/h ➡️ 1 as h ➡️ 0. Note, C = (x + h) and D = x. Substitution: lim h ➡️ 0 (2Sinh/2h)*(Cos((2x+h)/2)) evaluates to (1)*(Cos(2x/2)) which, in turn, evaluates to Cosx.

Really good

Nice video!!

you saved me 5 marks sin my alevel thanks

this video really reminded me on an older one of yours. you even said they're like homies. :) #YAY

Thank u sir ❤🎉

Doremon theme song in the background , so gooooooooood

Why can you bring the sin of x and the cosine of x out?

You can also use the expansion of sinx and it is very easy with that approch

This is pretty neat. #yay

Thank sir for guiding

I use the complex definitions

Thanks sir, well explained ❤️❤️❤️

Just a little question: Couldn't you just say cos(h) approaches h and sin(h) approaches (1+h) ? The result is the right one but we got the answer in less steps. #yay

Sir, What is dα/ dx of sec α

What is your language sir but teaching mathod is very nice

I still wonder how derivative of sinx can be cosx . Is it possible to proof the derivative of sinx is cosx from graph of it

well for the definition of the derivative i tend to do a "useless" extra step. i write the limit but the denominator (anyone with eyes will see why it´s "useless") i´ll write down "x-x+h" ofc it is just h. i´m aware of that. but i just want that pair of f(x) in the numerator amd x in the denominator and f(x+h) in the denominator ans x+h in the numerator just to show that this is nothing but the slope of a line between two points. and then, when this is clear we can kill the x-x in the denominator like a sensible human being and get to work but okay i´m a maths tutor so i show it to kids. Not adults who have their own fair share of mathematical knowledge. sow there is no need to link it to previously learned things this strongly. YOur viewers would appreciate something brand new as well as something build on a foundation they already have.

You are undoubtedly a cool human! 😎

I came here to understand a mug up 1step. But here he says to mug 10 steps ahh shit😂

how to prove derivative of f(x) = (u(x))^n?

Can you do an indefinite integral of cos(tan(sec(x)))? All calculators stuck on this.

Sir What is the answer of -d/dx cos x Pls reply me sir🙏🙏

Another alternative way to compute (cos(x))' if you already know (sin(x))', would also be to use cos(x) = sqrt(1-(sin(x))^2) and then the chain rule - works as well, I tried it. ;)

Which company 's markers do u use??

can you find the continuity (or not) of y=x^(1/x) from -inf to 0 ? I love your videos about complex #

Thank you ☺️

Amazing

Sir can you solve d/dx(e^x sinx) ?

Why was Doraemon theme playing on the background

Pls someone explain me 3:43 how (sin(h)-1)/h become zero because when I calculated it on calculator the value show very large.

We can also do this using Series expansion of Sinx then taking derivative of Intial terms

sin and cos are like homies : )

I wonder, what the full derivative of sin(a+b) is, since the full derivative of a multivariable function is more than just the successive partial derivatives? Mainly since layering the partials would simply give -sin(a+b)

i have a problem can you solve for me? solve for x x+[x]=1

Deja-vu: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-VMNX2xGffzU.html

Dude, but you did not proove the limits :(

sinhcosx on the third line dont get it wrong guys

👍🏻👍🏻

Where are my homies?!!!

Homies......LOL

baby help me

:v

First!