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Title: Quotient Rule

Added: Oct 4, 2007

Author: khanacademy

Duration: 9:31

Description:
Why the quotient rule is the same thing as the product rule. Introduction to the derivative of e^x, ln x, sin x, cos x, and tan x

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Channel: Education

Tags: derivatives  calculus  trigonometry  khan  academy 



derivatives  calculus  trigonometry  khan  academy 

Youtube Comments: 204

ULMORAIS Says:

Jan 22, 2012 - PLEASE, PLEASE, PLEASE make a list called "the magic of e", cause this thing is a very tricky thing =/In fact, the whole part of logarithmic and exponential functions is very difficult and there is not a list about it =(WHO AGREE VOTE UP =)

MrJapetheape Says:

Jan 31, 2012 - E just blows his mind @.@ hahaha

jocktheglide Says:

Feb 13, 2012 - I dont see how lnX equals 1/x. I did the ln of 20 on my TI 84 and then did 1/20 didnt equalt he same to me....then again my calc tells me -2 squared is -4.

Probesarecool Says:

Feb 17, 2012 - ... R U serious? the derivative of lnx is equal to 1/x I would prove it but I forget the proof

jocktheglide Says:

Feb 19, 2012 - yeah im being serious still dont understand it for some odd reason. Ill have to watch it again. In theory on paper how he writes I can understand, but when I try to punch in some numberson my 84 it does not equal the same.

satisfiction Says:

Feb 20, 2012 - "mildy lame" LOL!

EvilKillerClownMan Says:

Feb 23, 2012 - At 2:46... It looks like it should be to the -4, not the -5. You may want to check that Sal. Other than that, great job! I watch your videos daily! :) Keep it up!

ragabanation Says:

Feb 26, 2012 - @EvilKillerClownMan actually it's -6

Tranquilance Says:

Feb 28, 2012 - Well isn't x^-1 still there? But since the coefficients are -3, -2, -1, the next one is 0. Therefore it's just x^-1*0=0

R0adhead Says:

Mar 1, 2012 - My mind has been Blown

Vonlava Says:

Mar 2, 2012 - no...x^0 is is 0. the derivatives arent both zero..

Vonlava Says:

Mar 2, 2012 - that wasnt the derivative... it was the term itself...

s07106 Says:

Mar 5, 2012 - You have to change the -5th power in the beginning when you execute the chain rule when finding the derivative and change it to the -4th power

Tranquilance Says:

Mar 8, 2012 - What I'm saying is that the coefficient is zero, not the power, the power being zero would make it equal one, but since the coefficient is zero, the number has to equal zero regardless of the power.

Tranquilance Says:

Mar 8, 2012 - Basically, the derivative of x^n when n=0 is nx^(n-1)=0*x^-1=0

Spartan627 Says:

Mar 26, 2012 - I actually get kind of jealous when he starts genuinely having fun with these problems... I want math to be that easy for me :(

mja4201 Says:

Mar 30, 2012 - Mildly Lame

bkisme Says:

Mar 31, 2012 - I know, right? I lol'd.

CrimsonKunoichi01 Says:

Apr 26, 2012 - Are you a genius?

CertainHero Says:

Apr 28, 2012 - Sal loves E

CertainHero Says:

Apr 28, 2012 - So the derivative of my slope (high) on E, is contingent to the amount of E? hmmmm. "The magic of E" -sal.

soundersbloke Says:

Apr 29, 2012 - all the videos are green. why? i can't see anything

PhyOSPhyOS Says:

May 1, 2012 - It's not your calculator's fault, but yours. You can't put -2^2 and expect a 4, you have to write it as (-2)^2 so the power also takes the minus in.

LKRP92 Says:

May 10, 2012 - Do you yet have a presentation of why the derivative describes the rate of change of the original function?

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