Derivatives of Logarithmic Functions - More Examples

[seantopperharley]

Thank you very much, clear and well explained. Truly an educator.

[ThusIsBrad]

3:40 -4/3 right?

[teamjacobloveforever]

You, sir, are amazing. I understood this way more with your instruction, than with my own calc teacher.

[TheoryGL]

Incredible, I just searched for differentiation of logatithmic functions and I found this incredible video and it put me back on the right track for my homework. Great video!

Thanks Patrick!

[fanfanchau]

the answer in the last question hasn't been simpified yet.

ln2x-lnx=ln2

by the way,you are a very fantastic mathematics teacher and i wish you are my calc teacher rather than the one in my school right now....

[IRandomBeastI]

I wish I started watching these when the semester began...

[patrickJMT]

@IRandomBeastI i will still be here next semester : )

[samz2322]

you make math sexy



[LadyMacbeth22]

i wish you were my calc teacher....

[MoneyBoyTe]

thanks patrick sooooo much i missed a week of school in my ap calc class and came back today and was soooo lost... thanks to ya videos i got caught up on implicit differentiation, derivatives of log functions, inverse trig functions and logarithmic differentiation in a couple hours now i can actually do the homework thanks!!!!!!!!!!!!!!

[patrickJMT]

@MoneyBoyTe perfect! come back any time - lots of calc 1, 2 and 3 stuff. (about 85% of it is in the playlists)

[chrisford619]

How would I find the derivative using logarithmic differentiation of f(x) = x^x^2.

I watched exponential functions video but still not sure how to go about doing this qestion.

[cookiemonsterateYOU]

Why won't you multiply the derivative times it's original equation? I thought maybe you would take the natural log on both sides?

[classylilashley]

Can you please pose as me throughout my entire calculus semester and take my tests? That would be amazing.

[Themedjai2]

Patrick, your videos are brilliant! Thanks dude

[patrickJMT]

@Themedjai2 my pleasure, glad you like them

[BringMeToLife22]

I listened to a teacher talk about this for 47 minutes without understanding it. At the 56 second mark of this video, I understood it entirely. Thank you so much.

[BigMackes]

very helpful, i missed a week of school from being sick and you caught me up in 10 min, thanks bro

[patrickJMT]

@BigMackes happy to help. hope you are feeling better

[julianaboulos]

why cant use the properties of log on y=lnx/(1+ln(2x)) so it would be lnx-(1+ln 2x) ? please reply back!!

[emailaalice]

i've been studying for my business calc test tomorrow by watching your videos and i've began to develop a major crush on you! haha wish my luck!

[patrickJMT]

@emailaalice ha, super duper good luck to you! where your foil hat and i will try to send out brain waves to you!!

[martinezhmarcoa]

Dude! Thank u so much!! I have a test tomorrow. I owe u my grade and also thanks for uploading the helpful videos. I noticed u waste a lot of paper. For that i thank u lol

[patrickJMT]

@martinezhmarcoa i would not call this a waste...

[martinezhmarcoa]

@patrickJMT lol. I said that because of the paper that got stained from the top pages. Aside from that, it's not, by any means, a waste.

[patrickJMT]

@martinezhmarcoa well, usually it is all the same sheet that i keep below... : )

[misdrevenous]

I wish I was as good at math as you...

[patrickJMT]

@misdrevenous spend as much time on it as i have and you may be!

[julianaboulos]

why cant use the properties of log on y=lnx/(1+ln(2x)) so it would be lnx-(1+ln 2x) ?

[PerfectGonard]

@patrickJMT why did you do the chain rule at around 7:49, why isn't is just 1/2x ?

[Goukuhou]

lol, i was about to buy a calculus book. thank you, you saved me $50 with your videos and great site >:)

[imwithdumbhead]

Mr. Patrick, i'm spongebob, how many coupon bonds have you used for us? maybe try electricity things

[imwithdumbhead]

@imwithdumbhead follow up question, would you not be subtracting 1 from exponent 4? exponent rule? @5:33

[WTFMusicPerson]

I love these videos your the best way better than my text book lol

[SikderN]

I feel sorry for all those calculus students living in the dark pre-2008 era. Thanks a million :)

[blackjak9194]

Why can't real teachers be this good?

[5512048]

patrickJMT thanks alot iam from baghdad univercity and you just help to pass in final calculus exam

[rickyrubio94]

you sir, just saved my ass in my AP calculus class :)

[MiturBinlsderty]

might i suggest getting something to put under the paper you are writing on? That way, the paper below the paper you are writing on doesnt get the black ink dots.

; ) save da paper ya know

[stayfreshneverstale]

Sharpie should sponsor you.

[MersoBee]

Your sharpies are win. Your explanations are win. Your videos are win. You, sir, are just an absolute win!

[stephboeh92]

This was a great help!

[ApplePieIsEverything]

I really appreciate the time you take to make these videos, thank you so much!

[Aznmonkey]

This is all great examples! but i was wondering if u could help me with this problem.

(ln (1 - x^2))^3

[redsquarenine]

@Aznmonkey I think you would just do the inside and then use the power rule on the outside to get:

3[(1/(1-x^2))*(-2x)]^2

Makes sense to me, I really hope I'm right considering my test is in a few hours!

[redsquarenine]

@Aznmonkey Never mind, I'm pretty sure that was wrong and that you have to do the chain rule instead:

[3(ln(1-x^2))^2] * [(1/(1-x^2))*(-2x)]

[MisterTappi]

Nice video.A great refresher.Not sure why people would dislike this video.

[SIFYWAY]

hey thanks a lot my confidence i practice seems to be on a roll thanks again

[SIFYWAY]

hey thanks a lot my confidence in practise seems to be on a roll thanks again

[707firedragon]

i am new to this so how did u get the derivative to 1/sinx to be cosx?

1 more thing: can this be used with logs instead of ln?

[707firedragon]

i am new to this so how did u get the derivative to 1/sinx to be cosx?

[1220marksp]

TY so much for taking your time to help the world understand mathematics.

[CrueFest411]

absolutly awesome man. i learned more from u than my calc teacher. ur the man

[Ghareeb1412]

you are really my savior !

thank you X100000000000000000

[unclefroggyiscool]

great video

[xavs15]

i have a question i need to find the derivative of y = sin(2x)e^cos(2x) could guide me through ? thanks

[Jootube82]

Math 110 midterm tomorrow... thanks a bunch!

[hadd93]

Hey could you maybe do a video on rectilinear motion for Calculus. I know there's some physics involved but in my calculus course we're doing that and no matter how hard I try I can't understand it

[violentrixx]

MEW XD

[ChrisAmarillas03]

thank you for your video.....i lost my notes that we did in class and was completely clueless on how to do this....thanx for the help...you are a life saver

[XxSuperStreetxX]

this video is actually making derivatives of logs not that complicated. my textbook explains it in like 20 pages showing all the proof of the rules its so annoying. i should have watched this last night though, before my exam, because it sure would have helped.

[ChrisAmarillas03]

@XxSuperStreetxX my book is like that too

[salwa215]

First off, just wanted to say thanks so much for your videos, I remember using them for Algebra 2 and they were a help then too so thanks :)

Secondly, I have a question about the second problem that you did (the cube root of log base 7 x... when you were working out the derivative, would you not take the derivative of ln7 (since that would be 1/7) is that because it's like taking the double derivative?

[SOscar17]

I learn so much from your videos. My teacher is horrible and I'm using your videos to study for my exam, so thanks!!!!!

[FrankBooth99]

Quiz over this material in approximately ten hours.

Words cannot express my gratitude.

[mikelamid]

Hey thanks Patrick for your videos, they actually help unlke other videos on youtube :)

[patrickJMT]

@mikelamid glad you like them

[Krazyisthebest]

how would i solve -10^((6x^2)-7))

[ILOVEGIRLS808]

dang dude i love u. u got me through highschool calc and know im watching u to get through collage ha ha

[050942284]

thanks a lot

that's a good lesson

[2xiong]

Hi Patrick. I've subscribed to your channel and I've watched the first 16 videos on Calculus and you just made my life that much better!!!

You Are Awesome!!!!!

[sandra17143]

how is a logarithmic function figured out when its mixed with an exponential function like say

H(x)=2e^zlnz

[pizzainthehousse]

Just one question... unless my answer sheet is wrong, is the derivative of y= xlnx -x+8

y ' = 0? (since x(1/x) - 1 = 0) ??

[pizzainthehousse]

WOW! YOU ARE AWESOME! THNX SO MUCH! I have a test 2mrw and this REALLY helped me finish my review and understand everything!! THNX AGAIN!

[hviana7]

Patrick, you have been my savior in Calculus I and II. Thank you so much for posting these videos :)

[patrickJMT]

@hviana7 you are very welcome : ) go forth and spread the gospel about them!

[EatShanklish]

Thank you Patrick, I owe you and Salman Khan my A- in my Calculus course. Thank you guys for being so great and asking nothing in return.

[patrickJMT]

@EatShanklish you owe no one but yourself! : ) thanks though

[EatShanklish]

So log base a of any polynomial = (polynomial) ' / Polynomial ?

[galachoxy]

thanks alot from timor-leste,,,ur a great techer i ever seen,,

its very enjoyable to learn math with u,,thanks alot,,,,,,

[dragonmasta91]

if anyone say's ur videos suck, OMG, I WOULD SO KICK THEIR BUTT=D... your VIDEOS ARE EXTREMELY HELPFUL SIR! GOD BLESS YA x1000000000.

[YusefDeeb69]

you're the man!

[poopdeedoo123]

*phew* I usually ignore annotations... so I was confused for a bit. hehe thanks a lot!! For some reason my instructor refuses to just show us these little formulas , and the text book just implies it.

[kapranoshw]

Thank You Patrick, Amazing Teacher!

Cheers!

[dafterable]

thanks a lot from mexico

[DoctorRockso91]

you and your sharpie are an awesome team thx for the videos!

[shanerobertspilot]

you sir, are a god... that is all

[micisemo]

you are awesome thank you!

[Rohan233]

Any Integrating Logarithmic vids?

[sheeplauncher]

Thanks to your help i think i will barley get through calc one. Makes me sad i did so bad on derivatives and limits in the beginning but now im doing pretty well!

[lilmsunshine1]

I love you Pat! u save my life.

[lilmsunshine1]

thanks PAT! you dont know this..im a big big fan of yours. you made me pass my tufff calc course. you have helped other students along with me..dont ever ever stop making videos. Thankssss. :)

[Mustang5Speed]

Great Teacher! Thank you sir.

[Druhue]

Great information here. My professor flies through lecture and the book was extremely convoluted. This was concise and straight to the point. Nice work!

[420Z]

lol all those dots

[dxsam3]

THANK YOUU SO MUCH!

[PhunkKu]

1:15 - 1:46  why don't you write the derivative of g(x) anywhere?

[TheJawsusNSexmanShow]

grade 5 math

[dkingofny]

@qppdb123 when u bring a negative exponent from the numerator to the dynamometer it turns positive...

[julianjulianjulian7]

thank you thank you thank you! you are awesome at explaining things!!! you are my calculus savior!!!

[kangfuaction]

for the last equation don't you also have to multiple by the derivative of g(x)??!

[bassguitar00]

@kangfuaction not according to the quotient rule

[Deronoth]

He's like a free replayable tutor that I can listen to any time of day... awesome

[FatalKaos]

yes indeed, lil wayne has calculus tutoring videos too

[dumbdianaaa]

i really love you. legit

[Ilir7777]

really nice tutorial patrick but can you do one example of derivatiing the Llgarithmic functions like the last one you did on this video but making the equation with high exponents, so that for that last example of division we don't use the (g'x)(fx)-(f'x)(gx)/(fx)² formula but make it with the logarithms...i don't know if you get what i mean

[qpdb123]

why the power 2/3 became positive?

[qpdb123]

see 4:07

why?

[Ilir7777]

lol, simply because he put it on the denominator.

a^-1 = 1/a^1

[fes55555]

because you put it as the divisor...that what a negative power means...it's put under what's in front of it as the divisor

[heyboylol]

without him, we would be dead

not the real dead, but we would be dead in math test or exams!

[jimmysin10]

muchas gracias ... hasta que encuentro algo util en youtube..

GRACIAS !! Y SALUDOS DESDE MEXICO !!

[alisonip]

your hand writings is really good:P

[briggs150]

i love you

[tigercat00]

Thank you so much for making this video. You have really helped me study for my test. I owe you a lot!

[geovaniluna]

man, What would this world be without you?

a million thanks.

[chilltown3445]

it would be a Calcu-LESS world

[sonicboom23]

can you show, using first principles, how the derivative of ln (x) is 1/x?

Btw Im left handed too :)

[illegalmexican100]

we rule

[br0king]

nice name

[cw505]

that is where i lost him.

[endocringe]

you're amazing.

a million times better than my boring australian teachers.

thank you!

[jajaja295]

Australian high school maths teachers are balls

[XFiraga001]

Lol, better than the whole teacher being in front of the board.

What are yo writing on btw? Looks like the paper is on a pillow or something.

THnx for the videos, really helpful.

[ilovehuckabays]

your hand is in the way sometimes

[patrickJMT]

next time, i will try to make the symbols appear with my mind

[dragonmasta91]

@patrickJMT  LMAOOOO

[Theorinthe]

He's left-handed so it does happen a bit more, but you can pause it for review any time you like - that's the beauty of YouTube!

[stupidpablo1]

@ilovehuckabays

You can see through his hand just focus.

[poox63]

dude, you are a life saver. thanks for all your videos! do you have any models with differential equations? i seem to really suck at applying it to practice. cheers

[ouzairhafeez]

its simple and easy to understand......so thumbs up from me.....

[kartikyapareek]

Thanks a lott for posting these videos. Helped me for my exams a lot.

[theideachamp]

These videos are more useful than my class lectures-- no disrespect to my current professor-- but thank you, sir. This service is well-used and better appreciated.

[patrickJMT]

glad you like the videos.

i try to make them semi-useful, so it is nice when people let me know that they are : )

[patrickJMT]

also, it always makes things better when you can rewind : )

[dillon4321]

subscribed. your good vids will help me when I'm at waterloo next year

[undrgrnd12]

i see where u got the 2x,

but where did the 1 come from??

2x+1

[dillon4321]

If you are referring to the problem at 2:40 the derivative of x^2 + x is 2x + 1

(The derivative of x is 1)

[mansi45]

Thank you a million, you're really nice for doing this for us. one more thing, you have a very nice voice.

[LKJPDUR]

Actually i hate How you menupilate you voice too much. you should just let go, NOT HOLD BACK. (your voice).

[patrickJMT]

thanks for the truly worthwhile comment

[xxcowslayerxxx]

awesome

[KillaTequilla83]

omg thanks again dude, you're a godsend i swear

[xlwaiyiplx]

...

[pankajraja6]

thanks dear for videos,i m persuing b.tech.through correspondance so its help me a lot.

[iansdodge]

thanks! very helpful

[AutumnTeaLeaves]

At 1:43, isn't that f''(x) missing a g'(x) on top according to chain rule?

[KingofallCarrots]

that's why he put in the note.

[AutumnTeaLeaves]

Ahh. I see it now. Thanks :)

[HeyWheresKel]

I like how you went in there with annotations to correct your error. And I gotta say, your video is extremely helpful! It teaches me and reinforces the stuff that whizzed by my head in class!

[Arjun1234]

i mean 2:55

[Arjun1234]

at 3:13 how did u get 2x+1 to multiply with x2+2 ?? I'm just beginning to learn this, plz help?

[kiaracm]

2x+1 is the derivative of x^2+x

the derivative of x^n is nx^n-1

And 1/ x^2+x multiplied by 2x+ 1 is simply 2x+1/ x^2+x

[haseeb7882]

thank you patrick, your a good guy for putting up this video i have a test tommorow!!!

[initialg]

My final exam is tomorrow afternoon.

[illa2015]

honestly this and the easy way to remember the unit circle video saved me hours of memmorizing. Plus your other videos were a great re-fresher for my final today. Thanks!!

[patrickJMT]

hope the test went well : )

[illa2015]

haha yes i think it went well. seriously THANK YOU!!!

when i start calculas next week i will definitly be frequently checking out your videos on that :)

[jogavilz]

thanks!! you saved my life haha

[Beefstew2011]

Couldn't the denominator in the first example be factored as x^2-x= x(x-1)

[Penfish2k]

could that 1+ln(2x) be simplified in the equation at 9:24?

to be

y' = 1 - ln(x) / x [1+ln(2x)]

[sdnguyen10]

you should come be a calculus professor at UTSA...

[patrickJMT]

just move to austin : )

[Longmachao]

can i borrow your brain for my final?

[patrickJMT]

i would that i could sir

[jd637906]

can i do too?

[natzo89]

I got my final in 2 days, and you saving my ass bro!

[Ml11lON]

Lol, bro you're a champ, enough said.

[datuna]

haha, thank you so much.... you helped me a lot with many other things to!! :)

Tomorrow i'm having mid-term exam in calculus only on derivatives and I'm guessing what I'm gonna ger :P A..... hehe thanks (y) :)

[patrickJMT]

good luck on your exam my friend : )

[datuna]

thanks thanks thanks! I'm rushing now to the university haha :)

[knyawthwe]

hey man, I really have to thank you for showing the Derivative of Log. Everthing that you explained here, is all in my practice

exam. Thank you again. peace out

[patrickJMT]

happy to help - good luck on the real exam

[pinkcap]

thanks for the video man .. u kick major ass ;P

[grandalf111]

wow, this video really helps, going to have gce o level add maths tomorrow, so scared, this video really helps me

[patrickJMT]

good luck on your exam!

[ijumphurdles]

thanks pat