Quotient Rule Proof

[@zhixiantaivieve]

How can u be so serious and funny at the same time while proving maths😂 hats off doctor Peyam

[@blackpenredpen]

TAI ZHI XIAN hahaha totally agree!! I want to grow up to be like Dr. P!

[@zhixiantaivieve]

@@blackpenredpen hahaha hey sir , i watched ur videos too , it's great , both of u are funny and genius 👍👍

[@qubix27]

There is a whole Chinese derivative family of Chen Lu, his Italian wife Prada Lu and their son Quo Lu

[@ViktorKronvall]

Qubix The kid is surely named Quo Xian Lu, isn’t he?

[@jonasmb7]

More basic videos like that! Thanks Dr. Peyam :)

[@aracalbuto]

I'm not a mathematician but I like maths and your videos are awesome :) thank you Dr. Peyam!

[@LarryRiedel]

I like the horror movie camera angle. I was on the edge of my seat anticipating the jump scare.

[@frozenmoon998]

The Quo-Chen-Lu is amazing! When I first happened to come by it in my math studies, as they are not exponentially high or anything :)), I actually remembered a nice pattern, which states: Low, D-High - High, D-Low/ Square the Bottom, and away we go. Great video!

[@vtvtify]

A trivial proof that I thought of a few months ago: let f(x), g(x) (f(x)/(g(x))' = ? define h(x) = f(x)/(g(x) h(x) * g(x) = f(x) after taking the derivative of both sides: h(x)g'(x) + h'(x)g(x) = f'(x) substituting the definition of h(x) (f(x)/g(x))g'(x) + (f(x)/g(x))'g(x) = f'(x) after multiplying both sides by g(x): f(x)g'(x) + (f(x)/g(x))'g (x)^2 = f'(x)g(x) after subtracting f(x)g'(x): (f(x)/g(x))'g(x)^2 = f'(x)g(x) - f(x)g'(x) la finale, after dividing by g(x)^2: (f(x)/g(x))' = (f'(x)g(x) - f(x)g'(x))/g(x)^2 yay! xD

[@foreachepsilon]

I very much prefer the form (f/g)'/(f/g)=f'/f - g'/g so that I can say, "the relative rate of change of a quotient is the difference of the relative rates of change."

[@przemysawkwiatkowski2674]

K H Wow! I never noticed it! :-) Are there any applications of f’/f ?

[@foreachepsilon]

Przemyslaw Kwiatkowski I just think it’s more of a meaningful statement. It has logarithmic meanings too.

[@saatee100]

I am the sixth person enjoying your exposé!

[@High_Priest_Jonko]

I like to see more Analysis videos cause it's my favorite subject

[@otakarzdebski9497]

Why you are so much cheerful?

[@kobros-tech]

fantastic 🎉

[@yrcmurthy8323]

Sir, one thing. Derivative of (f/g) is derivative of (f • (1/g)). So we can just use product rule. Hence proved

[@drpeyam]

And the chain rule, so you need to prove the chain rule too

[@yrcmurthy8323]

@@drpeyam oh I see. Thank you sir. I didn't see that

[@michaelempeigne3519]

Would it be okay to do it by using product rule ? H(x) = f(x) / g(x) So g(x) * h( x ) = f ( x) And use product rule from there

[@drpeyam]

Yeah! That’s also a cool way of doing it

[@beatoriche7301]

To be honest, I don’t understand why many calculus teachers introduce the quotient rule when it’s really just as convenient to use the product rule. Is it your personal experience that introducing the quotient rule helps students? Personally, I am happy with just the product rule.

[@virajagr]

Can u please prove Chen lu as well:) I searched online and got only one proof that is dy/dx=(dy*du)/(dx*du) which gives us the proof. But can it be proved just by using the definition of derivatives(the limit of h tends to 0) without introducing dy/dx? Thanks

[@drpeyam]

Already done!

[@virajagr]

@@drpeyam oh I didn't notice it, just watched it thanks it was awesome:)

[@VibingMath]

A very solid proof from first principles, compared to your other videos, this is only on kindergarden level 😁

[@RalphDratman]

Exactly. And, way back in calculus (at Berkeley!) I always had trouble remembering the stupid quotient rule! So it is very pleasing to me to see it demonstrated so gently. Dr. Peyam, you are a good man.

[@turbopotato4575]

There is another proof that is easier far more intuitive in my opinion: First apply the product rule to f and 1/g the use the chain rule on 1/g

[@Silver-xf7it]

You have a new subscriber

[@drpeyam]

Yay!!!

[@phronessys]

It's exactly what i'm seeing in college, thx

[@rigorless6330]

based on the camera angle i kept expecting everything to slide to the left the whole time

[@mikedavis8973]

Quotee Lu!!

[@Flanlaina]

Use the Quo Chen Lu!!!

[@jayamitra4656]

Next paw-duck rule.

[@tusix6]

My gf is like the sqrt of -100 A solid 10

[@shashwat4920]

Copied

[@GRosa]

Or an imaginary 10 😂😎

[@Flanlaina]

Shashwat 10*i, where i is the imaginary unit

[@benjaminbrady2385]

Quo Chen Lu

[@RalphDratman]

I had some difficult studying the board each time before you erased it. I kept having to pause whenever you moved out of the way. Could you please write higher up on the board so your body will not be in the way of what you have written? Or in some other way provide more time to read what is on the board. Thank you. (PS I love this very much)