Logarithmic Differentiation

[lovelyanimeangel]

i was actually excited to learn from you! Thank you so much for everything

[MrTieoken]

Where can I find a video about logarithmic integration, I might be missing the title on your site though? In any case, thank you.

[ThePsionicMatrixTM]

he is the man !!! aye Patrick, can u please add a search par to ur website so that it is easier to look for something, im having a difficult time looking for specific stuff on there.

[Jo00j0oo]

dude, seriously thanks

i believe u will rescue me by your math videos b4 my exam

thx again man

[gethisoverwithit]

i really love the fact your work is very clear and detailed. Also, your explanations are really on point. i never failed to follow your work.

all in all, you are so much better than my math teacher x.x

[rockrgrl637]

I used to know how to do logarithmic differentiation... then I took an arrow to the knee.

[solde99]

Adictive!

[vampiracy]

Hey Patrick. I like this technique and find it really useful. I would just like to provide the explicit way of doing this derivative, using multivariable calculus, in case you or anyone else reading was curious. First you rewrite y=ln(x)^x as y=u^v, where u=ln(x) and v=x. You then use the chain rule -- ∂y/∂u(du/dx)+∂y/∂v(dv/dx) -- and you will find your derivative to be ln(x)^(x-1)+ln(ln(x)) ln(x)^x, which (after factoring out ln(x)^x) is the answer you got. Thanks for reading! :)

[djd259th]

I wonder how many of us would fail calc2 if it weren't for you... 

You're a lifesaver. Thanks again!

[Marcuzzorox]

Specially if you have a giant product derivation to solve..

[Marcuzzorox]

This technique is very useful!

[Jozekban]

Math with Patrick everyday

keeps your teacher away

[CharlahMurphah]

Hey Pat, you should totally put this in your first semester Calc playlist! Thanks for all the help!

[DragonCawk]

I could of learned calculus for free by watching these videos instead of paying the tuition I do now for some fancy university

[BellaMrdch]

i visited your website... i have to say, you have an impressive amount of videos. I've only watched a few of your videos but i do think they may be able to help me for when i sit my IGCSE addmaths exam. So, "thankyou" in advance:)

[OhHiMeMatt]

hey pat, why is the natural logarithmic function y = lnx used much more frequently in calculus than the other logarithmic function y = log a x?

[redrum41987]

@OhHiMeMatt because its deriv. is 1/x oppose to log a x which is 1/x(lna)

[pirfarator]

10 stays because it's a constant

[pirfarator]

HUGE THANKS!

[cristian616]

I appreciate the help and all but you should invest on some other type of recording that your hand doesn't cover the work.

[StarlightOnly]

I love calculus! My teacher is as good as you are to teach differentiation, so he makes me understand everything. It's my absolute favourite class :)

[OhHiMeMatt]

@StarlightOnly impossible! no one is as good as pat :)

[StarlightOnly]

@OhHiMeMatt I'm telling you ! It's like Pat had my teacher =) Still it's impossible because I live in Quebec but you know! (: I SOOOO understand that :D

[sulmazz]

If I ever had to teach calculus - I would watch your videos and then just mimick everything that you say and do down to the T !! thank you for helping soo many of us pass and even start to enjoy Calculus

[patrickJMT]

@sulmazz glad i could help : )

[HimeMurasakiPrincess]

@sulmazz hey why even bother talking? just sit down and let the stdents watch it :)

[Spiceman333]

Love your videos.. but where do I look if i want to find out how to diff something like 2^(x^2)?

[patrickJMT]

@Spiceman333 derivatives of exponential functions

[Supermodoz]

thanks ^_^

[S3an81]

why does the 10 stay?

[longdarie517]

Thanks so much man. You saved my life

[lizhiwen20]

Very helpful! thx

[VictorAndScience]

When I get my degree, hopefully in the time it's intended.. I wanna be just like you Pat... Helping people get smart, always with pretty fingernails.

[XangelkatzX]

On an unrelated note: The very fact that the speaker is left-handed perturbs me, Nonetheless, this was great :) Thank you so much!

[patrickJMT]

@XangelkatzX i always try to use jedi mind trick to pick up the pen with my mind, but it has yet to work.

[falcon00135]

how do u know when to "ln" both sides?? and how do u know wen to replace the "y" with the equation tht u first started with to finish off the problem?

[MichaelKumove]

@patrickJMT you are my mathematical hero



[tomyo669]

this video is popular in: Ethiopia what the fuck?

[superman3621]

i think i love you

[mikelillo1000]

Why don't you apply the derivative to the number 10? On the fifth line you apply the derivative to each term but not to the number ten, why not?

[Wemadesomevideos]

@mikelillo1000 If it was just 10, he'd derive it to 0. But since it was 10(ln(x^2+1)), he used the product rule on the whole thing, which gives 0*ln(...) + 10 times the derivative of ln(...). So he did include it, just as part of the product rule. Hope that makes sense. It's 5 a.m. I may well be babbling.

[cooldude8081]

An awesome video.... :-)

[angelinbluejeans80]

PATRICK: YOURE GOD.

[sinchamp]

what is 2 - 4 + 8 then / 1 lol joking p.jmt u are a legend! ur vdios are wonderfull and easly understod =) thank you  a bunch! (Y)

[bodinian]

If I want to scare someone, I don't take them to see "SAW", I show them my math homework

[mychemicalwhatever]

i wish i knew of your videos a little earlier than the day before the AP exam. :P awesome explanations though! Thank you!

[alicetex]

Hey Patrick, video is not working, thanks

[pharmacyanastasio]

you said that e^x is just 1, but you didn't write +1 you just skipped over it and continued to write the 10...since it is adding that you were doing there, shouldn't the 1 have been added?

[pharmacyanastasio]

@pharmacyanastasio sorry I mean lne=1 not e^x but the question still stands

[Johannalovcheese]

@pharmacyanastasio He was multiplying the to the x^2 because they were a joint function.

[ndrwplussine]

How do you differentiate log x to the base b?

[heavengirl]

You give me hope! :)

[mcorvi12]

this vieo helped me so much i cant thankyou enough

[Gujarbrumtown]

hi patrick need help wid defferenciation when given an equation which has X and W if u know wot i mean.. when u have to seperate the equation into DY by DX and DY by DW for instance.. would apprecaite it if you could send me a link to a video which adresses thjis problem ... thnxs

[MetalupyourArche]

I normally don't have any problems with derivatives but there is one exercise that has been bugging me all day.

√x (^5log x³) ...

Using the chain rule I get (lnx³)/(2√x ln5 ) + √x . (1)/(x³.ln5) .

However, according to my text book I only got the first part right... I have made this exercise over and over again but i still couldn't get the solution to fit!

If anybody could explain me what i'm doing wrong, it would be amazing.

[SamYeow2102]

you rock! this totally helps me alot. thanks =D

[swimmerfurlife]

so you said it was incorrect method at 6:10 but why?

[vehiclerandomvideos]

How do you solve 4^(x+3)=7^(X-1)?

[patrickJMT]

@vehiclerandomvideos you use logarithms. i should have videos on solving exponential equations somewhere if you do a search on my videos on my channel

[invariant144]

@vehiclerandomvideos First, domain, x cannot equal -3 nor +1. Next, take natural log both sides: (x+3)*ln4=(x-1)*ln7. Next, distribute the constants ln4, ln7. You should be able to solve with ease

[rshrott]

@vehiclerandomvideos take the log of both sides

[makelifeprettiie]

thank you for this!

[green1375]

Hey Patrick, what happens to the 1/y on the left hand side?

[makelifeprettiie]

@green1375 you multiply by y on the left side to cancel it out, and multiply it also on the right hand side.

but because you want all your terms in x, you sub in the value of y which would be the original question.

[noobguitar321]

7:23 I can actually cancel my "exes" out

-that got me hahaha :D

[dajakesta1234]

uhh so anything that has to do with ln is gonna b the recipricoal of itself???

[thewhitesmith]

All I needed to hear was then we do the product rule. Thank you!! Haha

[skylermiller29]

You sir are a savior, your video has taught me more in 8 minutes than my college professor has in 16 weeks!

[cowboyzfan713]

log( 2 - 3x)=3 ??????

[patrickJMT]

@cowboyzfan713 there it is

[Tavi13]

OMG you're Godsend, You explain things so much better than my professor. Who needs going to class when I can watch your videos. thank you is not enough but thanks.

[1991nadia1991]

Thank you so much! I have spent forever trying to go through this but I just couldn't understand what my lecturer was on about, but you make it sound so simple!

[ghostf779]

I don't care how well it's explained... my brain hurts... I use to think math was easy until I went to algebra and trig.

[ikmal017]

math is hard, tommorow is my add math test, i dont know if i could make it

[rubixAid]

i love you and your math and the whole fucking univers

[iniloy1993]

how do you know when to use it?

[matthewzoot]

your x looks like a multiply... you should consider using an algebra )(

[Jahkrel]

@matthewzoot x's are replaced by dots or brackets when working with algebra to get rid of the confusion.

[alnilam54]

why isn't it 1/2 lnx ^-3/2? do you not have to take the derivative of sqrt x? Thanks for your implicit differentiation videos.

[gingkapu]

Sir! can you answer my assignment 3x^3sin^2(e^x+y)-3x^2tan(ln^2 x)=e^x/e^y-e^-x ?

Thank you very much!

[pinkybill2003]

how come the constants are along for the ride? why don't you take the derivitive of them and get derivitave of a constant which is 1? about 3:18

[patrickJMT]

@pinkybill2003 the derivative of a constant is zero - you can always use the product and see that you get the same thing

[idaho777]

@pinkybill2003 derivative finds the slope of that function.. if you find the slope of a constant, it's always a horizontal line

[ommy7778]

@pinkybill2003 if you know more why dont u post video?

[pinkybill2003]

@ommy7778 i was asking a legitimate question- i'm trying to pass a calculus class here. i was thinking the derivitive of a constant was 1, which i was obviously mistaken about. its zero.. patrickJMT answered my question.

[rumpleskillsson]

@pinkybill2003 i was thinking the same thing

[ikmal017]

thats what i'm studying now in class, hell of confusion

[Volcin]

great video.

[Danasqu]

thnxxxxxx aloooooooooooot (F)

5^100000000000 *

[MissKaroliukas]

Love you PatricJMT! That is very helpful video.

[shinemooon]

awesome

[SuperhumanChichi]

Actually, forget my last question. I get my mistake now. Thanks :)

[SuperhumanChichi]

I have a really stupid question to ask but.... can someone please explain why @ 2:07 why the 10 Ln (X^2 +1) isn't to the 9th power? I was sort of thinking that chain rule is done there, but I was perplexed as to why the exponent disappears entirely. If someone can explain why this happens, I would really appreciate it

[HemantKumar83]

This is for others who might be wondering : He isn't using the power rule. It's simply a property of logarithms. Bringing the exponent of the term that you are taking a logarithm of:

ln(x)^10 = 10 ln(x)

[Yu2Kal]

@SuperhumanChichi Its a property of logarithms you can take powers infront of the log, like Ln(2x+1)^5 = 5Ln(2x+1), he didn't differentiate the right hand side yet, hes just simplfying it, hope I helped =]

[elten400]

super

[Ndlovukazee]

m ryting my test in a few hours from now....m glad i saw this b4 ryting!tnxalot!

[yonatanalemayehu]

Wonderful demonstration...

[aparrotslife]

Patrickjmt is my savior!!!! Thanks for helping me get an A in my calculus class...heh is awesome.

[pernellius]

i used to be scared of logarithmic differentiation... i always skipped problems if i saw a ln or an e. thanks to your explanations, i now appreciate them as a shortcut and am not so intimidated :))

[JayZeus7]

After every Calculus lecture I watch your videos to gain a greater understanding of the subject being taught.

~Thank you for these videos to help me learn and enjoy the wonderful beauty of Calculus!

[jpd4]

This is awesome to watch high.

[injn0719]

you have such neat handwriting..and this totally made things clear. thanks=)

[username14657]

Thaaaaank Yoooooooooou!!!

[600187]

thank you

[mistabrown714]

great video!!!!!! dude ur math gifted lol

[utubegay1]

there is no such thing as math gifted its lots and lots of practice and hardwor

[AhmadAshi]

Thank you so much!

this helped figuring out a solution for the heat equation!!!

thanks again:)

[FlavouredVitamin]

You sir, are a life saver!

[arikatz]

hi you say that in the example

y= (lnx)^ x.

Then you say that it would be wrong to proceed as follows:

Y = x (lnx)^(x-1).1/x.

WHY IS THIS WRONG?

[Rib640]

@arikatz I'd also love to know... =\

[countryslicka]

hey, i need to find x for an integral problem: i've solved it down to 1-x^2=3lnx and i can't figure out what x is equal to

[TFitty2020]

karlkarl dy/dx is not a fraction it simply means y' the answer to your question is no

[karlkarlkarl1234]

Question:

Does dy/dx × 1/y = d/dx

?

[GinoftheWind]

No. 'dy' is a derived term of 'y'. They are not the same thing and thus one cannot cancel out the other.

[heyyhowyadoin]

even though you dont use fancy stuff like that other calc guy u still kick ass in teaching it

[Gengar3084]

blow it out your ass cookie

[CookieWalka]

you leftys disgust me

[shabobbit]

thank you so much!

[dxklRandomhl123]

Thanks =D, my teacher made this seem a lot harder than it really was.I am thankful that I still have several months before I take the actual AP exam (so I can also use videos like these to help me).

[khalid02006]

Iam from Saudia Arabia. I also got improved, watching this vedios. I just wanted to say thanks alot for this brilliant teacher.... and good luck for you guys .....

[hasben0]

plz keep posting these vidoes, i have improved alot in my calc class just from watching these videos. your the best teacher ever.

[Yaemes]

I wish you were my teacher...that was really easy to follow

[tigercat00]

Thank you! This was very helpful

[MASTEROFPUPPETS238]

LEFTY FOR LIFE

[jm118107]

thanks man!! your awesome!

[gandy2392]

i wish you were right handed

[mjay22]

If it's so boring, then why are you watching it? there are other videos that you can watch that you may find interesting. It's probably that you don't like the necessary details that he's going to so that he can try to help us understand such complicated maths equation like this in an effective way. I myself find this man helpful.

[Kpathma]

Awesome tutorial. I used to be able to do this sh*t in my sleep. Now it makes my brain hurt... damn I should've kept on top of this stuff!

[pcj25]

ello, I am Gaston of Argentina, study Engineering in Perforations. The topic is really easy. Excellent explanation. This topic we study it in the first four-month period of the first year.

[Sunny066]

your a champion! thankyou so much

[christl301]

I can not do maths at that level, but looks really cool.

[boorens18]

yes you can...just takes a bit of practice and memorizing the rules

[christl301]

Okay will give it a go, so just checking when you add numbers the sum gets bigger or is that subtraction.....lol

[iTormenTi]

Depends whether the number is positive or not.

[thelonelydandelion]

this helps me. Thanks.

[ertxz18]

I need some help, I am trying to find the derivative of y=x^-cos(x) using logarithmic differentiation. my final answer was y'=y((sin(x))ln(x)-cos(x)/x) but got it wrong, at least the software says so. Did I do something wrong?

[Kakashinoor]

How would I do 3^x^2 and 2x(2^x) ?

[jackeddemon]

>on the right....

i lol'd

[Kakashinoor]

5:08 lol using sharpie has got to suck

[bebexlefty]

Thank you!!!!!

[skoob6969]

Know your busy but what about 4^x. a number with a variable exponent.

[lfrae]

thanks,

you made that incredibly clear

[danisarno]

thank u very much...I appreciated your help...!! you are very good! I LOVE MATH TOO...BUT I HAVE A LOT WAY TO GO YET!!!

[01supra]

idk how u got the 20? yea i no i got i hard head when it comes 2 math

[MikeyR0101]

The 20 comes from multiplying the 10 with the 2x.

10*1/(x^2+1)*(2x)=(20x)/(x^2+1­)

[nickihous]

thanks a million! quite a big help. you're voice is cool and the video is fine.

btw, can you make a lecture on 'Differentiation Under Integral Sign' for college student(12th grade in US curriculumn) I read about it in the book-'Surely you're joking Mr.Feynman' I really wanted to do this as I read that, but I can't understand that with only help with wikipedia. If so, I would feel "thanks a billion!"

[utuber6600]

just for a laugh half way through your videos you should change to a london cockney accent.

i'm sure it would make you more appealing to a wider auidence.

ace vids btw.

[pgriffith4]

given f(x)=x^e  find f ' (x)

answer: ex^(e-1)

why is this different than the incorrect example shown at 5:50?

[patrickJMT]

because e is a number, x is a variable

[pgriffith4]

thank you

[Sirstompington]

Thank you soo much!! this helped me on my math homework

[henricx1]

this is better than porn

[1a1a2a3a]

lol...

[04sheepy92]

lol...

[patrickJMT]

i dunno.. depends on what kind of porn

[amara01addis]

Japanese girls puking in each others' mouths.

South park is twisted....

[MrMig3]

@patrickJMT hahaha your awsome

[MetalOmgz]

@henricx1 lmao

[MuchachoInca]

Gracias!. Thank you! TE AMO

[Tyme1v1aster]

This is on your playlist twice, you should take it off #8 lol.

[magitronic12]

for the second one i think the answer should be

y ~ = (lnx)^x (ln(lnx))

[k0tl]

to Tyme1v1aster, the process hes using is a combination between using logarithmic laws and implicit differentiation to find horrible long ass derivatives of certain equations, its not CHAIN RULE :)

[xxxmagixxx]

just awesome!

[potasiumpermanganate]

Thank you! YOU'RE FANTASTIC!

[ultimate133]

can you come do my math test for me tomorrow?

i'm joking. but i do have a math test tomorrow. and this helps quit a bit! thanks :D

[ddd1600]

ahhhh you are the math Bodhi, I've been staring at inscrutable jargon and incorrect answers for hours. Thank you so much

[interfc118]

I admire you dude! thanks for the video!!

[HeyWheresKel]

"My 10's along for the ride"

I like how you word things.

[anthonychemistry]

please explain ln e^X2 = X^2

what properties of natural logarithm is this?

reply please..

[guitardweep13]

Natural logarithms are logarithms to the base e.

So just as the base 10 logarithm of 1000 is 3, as in, log(10) 3=10^3 Ln = Log(e)

Log(e)e^x^2=x^2

The simple way of thinking about it is that having the natural logarithm and the e cancels the two out.

[k0tl]

to "anthonychemistry" lne^ X2 = X2 lne

and also lne = 1

therefore lne x X2 = 1 x X2 = X2 :)

[ruleas2kings]

why do i have the sudden urge to make love to you after seeing this video?

[patrickJMT]

smart = hot

[lafan805]

where does + 10 come from?

[Jordan4Jesus4Eva]

This is incredibly useful! You are great at explaining things and crystal clear. :D

Thank you.