Quotient Rule Proof

Proof of the quotient rule from calculus, using the definition of the derivative. This is a must-see for calculus lovers, enjoy!

[zhixiantaivieve]

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

[qubix]

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

[jonasmb]

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!

[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

[LarryRiedel]

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

[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."

[beatoriche]

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.

[frozenmoon]

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!

[saatee]

I am the sixth person enjoying your exposé!

[High_Priest_Jonko]

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

[yrcmurthy]

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

[VibingMath]

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

[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

[michaelempeigne]

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

[turbopotato]

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

[phronessys]

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

[rigorless]

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

[adr]

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

[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)