วีดีโอ

nonsense... you are dividing by zero...

Real analysis 🗿

Uh...how's this a proof? To prove something you need to start from scratch...this is just a way to justify the topic in the video...not a way to actually show that this is true. You used already existing exponential rules, without proving their existence throughout.

x^3 = x*x*x x^(-3) = (x/x)/x

I... this isn't a proof, this is a justification for the *definition*. Negative exponents are just another notation for the same thing.

nice. But fyi, the video becomes blurred after about 30 sec

You need to define square root more carefully, and you need to specify what a and b are. IIf a=-1 and b=-1, then √a√b=-√(ab). @2:41: "the square will cancel out with the square root". Not necessarily: square root of x^2 is not x, but |x|.

Other Useful Videos: Power Rule Proof: th-cam.com/video/9SJrITmqrA4/w-d-xo.html Product Rule Proof: th-cam.com/video/MhiiW2SGd_w/w-d-xo.html Quotient Rule Proof: th-cam.com/video/gXB8wMADpec/w-d-xo.html Chain Rule Proof: th-cam.com/video/PweHLa0R88Q/w-d-xo.html

To make this proof work, you need to define your square root a bit more carefully as the unique positive number that squares to the argument under the radical.

The cleverest and simplest explanation I've seen for this topic! 👌

U deserve a smooch for explaining this so cohesively. thank you

Thank you, it's very helpful for beginners to know the reason why they have the negative ab there-cancelling the other terms except the cubed ones. Maybe for the next part you can explain the a³ - b³ prove..

It is fine. Thanks.

Wow, thanks for the info! 🎉❤

Gonzalez William Perez Linda Martin Mark

While I agree with your solution and a majority of the solve. I think it would be remiss if you didnt include the reason that you did the division before the multiplication. Its not because the D comes before the M but that in order from left to right it came first. If there was a multiplication on the left of the equation is would be completed prior to the division. Same holds true for the addition and subtraction.

Thx mate

b 9

Truly incredible.

Awesome explanation - super clear and quick 🙌

Thx bro

This proof relies upon Pythagorus' theorem. So to be a rigorous proof you now need to prove that (without using Sin^2 x + Cos^2 x =1).

0¹÷0⁰=0¹ 0¹=0¹(0⁰) 1=1(0⁰) 1=0⁰

Prove d/dx of C is xero.

Wouldn’t you have to use the epsilon delta definition of a limit to prove this?

Doesn't x = 4???

Being nice here: Imagine if the RHS had a Sqrt of it. We don't know the lhs function in [] .. how would you solve it? No Hyperbolae.

Squeeze thrm

Wow so basically its a lot like multiplying by the conjugate. Which is just a fancy way of multiplying by 1. Calc is so interesting. Thanks for the video.

4=8^x 2²=2^3x 2=3x X=2/3

._.

Sin2x=Sin(x+x) =(sinx. Cosx )+(Cosx.Sinx )... {Sin(a+b)=sina. Cosb +cosa. Sinb) =(sinx. Cosx )+(sinx. Cosx ) =2.sinx. Cosx (proved )

If you know about complex numbers, you could also use the complex exponential form of cos and sin : -> cosA = Re(exp(iA)) -> sinB = Im(exp(iB)) And use the fundamental property of the complex exponential : -> exp(iA)exp(iB) = exp(iA+iB) starting formula : cosA sinB exponential form : (exp(iA)+exp(-iA))(exp(iB)-exp(-iB))/4i expand : [exp(iA+iB)-exp(-iA-iB)-exp(iA-iB)+exp(iB-iA)]/4i reverse the exponential forms : [sin(A+B)-sin(A-B)]/2 This approach is extremely powerful and can be used to prove any trigonometric identity I can think of.

Here's a trick Since arctan (x) + arccot (x) = π/2 π/2-arctan (x) = arccot (x) Differentiate both sides We get 0-1/1+x^2 = d/dx arccot (x) So the derivative of arcot (x) is -1/1+x^2

do u know the real proof?

That’s not a proof, that’s one way to solve it

Wtf is this voice

Now prove why sin(A+B)= sinAcosB + cosAsinB

Thank u so much brotha❤❤🗣🔥

d[f(g(x))]/dx= (d[f(g(x))]/dx)(d(g(x))/d(g(x))) = (d[f(g(x))]/d(g(x)))(d(g(x))/dx) =f'(g(x))g'(x)

Great video big man, real easy to follow. You popped off fr 🗣️

Great video man! I am surprised I could understand a calculus proof this easily. Underrated youtuber fr 🗣

I feel like Barney Gumble is explaining math to me

sqrt(1+y'^2) use trignometric substitution y'=1sectm dy'=secm.tanm dm dx=dy' length=integral of (sectm.tanm.tanm) ......

cos(a-b)=sin(a)*sin(b)+cos(a)*cos(b), cos(a-a)=sin(a)*sin(a)+cos(a)*cos(a), sin(a)^2+cos(a)^2=cos(a-a)=cos(0)=1

great video!

Hmm a british explaining trignometry,what was i serching for 😅

surely using the sin^2(x) + cos^2(x) = 1 formula is easier? its shorter and is easy to show true from the unit circle

you noob

cos²x+sin²x=1 Divide by cos²x 1+tan²x=sec²x Done.