Calculus: Logarithmic Differentiation

[clay12349876]

im hard



[veeds74123]

my calc final is tomorrow and you just helped A TON. Thank you thank you!

[jonesmm3]

*mid-term

[jonesmm3]

Who are you and where do you teach...? I got a 100 on my Calc final because of you.

[xheather492]

The night before my much-dreaded Calc I final, I finally get clearer explanations of these concepts.

And... this guy is so calm!

[nickrohn93]

@xheather492 How did you do?

[rhondal9w]

I love how organized and clear he is!! 

[themoonstoneassasin]

when he says "log" does he mean "ln" (natural log) since it seems that is what he writes?

[fishraw]

@themoonstoneassasin yes

[rhondal9w]

@themoonstoneassasin, Yess. =]

[pg6661]

@themoonstoneassasin

Yes, he does mean natural log when he says "log".

[23SuS23]

this guy is fucking awesome.

[the7ouch]

this guy has amazing eyebrows

[UltimateSAB]

sir, you are amazing!!!

[Jeweettzelluf001]

you can read a book, or you can just watch this video and save time. I prefer the video

[viadude2011]

Great video, thanks!

[wikenator]

this is NATURAL log differentiation, not just logarithmic differentiation.

[gushortle11]

Firstly this is a great video you explained what took my lecturer 50 minutes to explain in 10 minutes and in a more and clear and concise manner then they could.

I do have one query however, in the final example where

y = (ln(x))^x

why do you take the ln of both sides? Could you simply use the property of logs and have

y = x * ln(x) ??

and save yourself some time and an exam?

[rockandswing1]

@gushortle11

Be careful. It's true that Ln[(x)^x] is the same as x.Ln(x). But this prof is talking about [(Ln(x)]^x. Look carefully at the difference and you will understand he is not wasting time.

[vincemarcus1]

i take that Back its cos x not -cos x....

[vincemarcus1]

I thot the Derivative of sin x is -cos x (a Negative Cosine X)?????

[zennerkind]

Why can't my teacher be like you? the world is not fair!!!

[BlueCoolWoo]

I wish you were my teacher :(, you're amazing at what you do.

[trimoth95]

(y)

[Baserux]

omfg are you a genius?

[trimoth95]

@Baserux I was wondering the same thing while watching this vid -_- haha

[decep01]

y=e^9x cos x

i got 9 ln x sin x

[airport1207]

ur my hero. love you

[blinddogroofer]

As an aspiring secondary math teacher, I want you to know I very much appreciate videos that you and others have uploaded.

[chronicconnection]

thanks man you're awesome

you make it so much easier to learn it

[ilasttt]

thank you, wish i had you as my teacher. Your great

[riggskoh]

This is great! This is the only logarithmic differentiation tutorial that tackles the basics. Calculus made easy!

[ndrwplussine]

how do you differentiate log x to the base c?

[badwan92]

YOU'RE AWESOME ...!

[JonasAdeline0107]

IDOL!!!! ^^

[Dmenjivar22]

great stuff

[yeahmoik]

genius!

[bodinian]

At 5:40, could you take sinx/x and replace it with 1?

[karwansindi]

Thank you, you make math really easy

[PitongKandule]

is this the same y` = dy/dx??

[riggskoh]

@PitongKandule yes. dy/dx is the Leibniz notation of y'

[ashleysmithd]

Great video. Thanks.

[omarmohali]

That was awesome

[xCoreProductions]

Thanks. You're going to help me pass my final

[Osman9100]

Thank you

[AC33592]

Messing this up is as easy as (heh) falling off a log.

[marchingbanddude]

another easier way to do this is: for example: 5^x, you rewrite it, times the derivative of the exponent, times the ln of the base. so in this case it would be (5^x)(1)(ln5). another one would be x^sinx. (x^sinx)(cosx)(lnx). just saying

[cloudxpeaches]

OMGAH THANK YOU!!!

[wishkah256]

Amazing, thanks a lot!

[JudgeAxe]

There's a hero.....if you look inside your heart. You don't have to be afraid, of what you are................YOU ARE GREAT AND I LOVE YOU!

[timmytankTK]

how come the chain rule is used for xlnx but not xln5

[ataggake]

@timmytankTK

Because ln5 is a constant so differentiating xln5 is no different from differentiating 3x

[MISTofDAN]

@timmytankTK Well a chain rule is used but if you differentiate ln5 then you get 1/5(0)=0. So you should know that you need an x value after the ln or its automatically 0.

[comecra85]

but what about constrains?

[yukyisan]

YOU ARE THE BEST! I think my calc teacher can't teach me anything.

[djelite07]

Can you show us how to make a time machine out of delorean ;)

[dmonnin]

8:33



[Yu2Kal]

@dmonnin wat about it

[cndnby111]

You are so my hero!

[SheepRCool17]

SO helpful

[Gizmotech48]

wait, on the first problem, how did he know the derivative of logy was 1/y? is it just a rule that i haven't learned yet?

[12edDemon]

@Gizmotech48

Yes, the derivative of a natural log "lnx" is 1/x

He uses the chain rule though, so lny is 1/y times the dirivative of y with respect to x, which is unknown, so we write dy/dx

[islaamisbeuty]

excellent explanation!!! do you have any lessons on trapezium rule! thanks

[makmegs]

maths, my worst enemy and this guy, my best friend as of today :D

[aparrotslife]

You are brilliant!!! Thank you, thank you!

[rctriplefresh5]

how the fick do you get so smart so that you can teach calculus like its cake? im in college and am failing precalc, although i dont do homework, but my teacher hates my guts so i dont see the point. im a math and science major but i hate amth and science. i wnt to do psychology but i heard it sets you up for a job at burger king alsio.

[engrgirl322]

The people who teach did their homework and had a positive outlook on their class, despite the teacher teaching their class.

[Grandpagimp]

@rctriplefresh5 You get smart by hard work and practice. You should do what you love, and if your good at it, someone will pay.

[brothadave]

Thanks so much. I'm taking the gateway exam for calculus today and this helped refresh my knowledge greatly

[TheMali18]

i need help with logarithmic differentiation can anyone help?

[stepbil]

He is great. The purpose of this tutorial is not to show u how to apply rules blindly but rather how to differentiate and being able to justify ur answer, breaking it down into more understandable steps.

[y2kbug77]

What about when there is no exponent? I have problem that is: Find The Derivative of y=ln (x^2 + 5x)

[LuckyT421]

wouldn't the chain rule apply?

[vrchacho]

Yep, I got my derivative wrong. It's the derivative of the logarithmic arguement times the logarithmic derivative. So it's 1/(x^2+5x) * (2x+5)

[vrchacho]

The last (2x+5) is multiplyed by the 1 in the numerator, forgot 2 brackets on the fraction.

[jerrywu78]

@y2kbug77 just use chain rule and derivative of ln x is 1/x

[pimpimbulldog]

use the chain rule, y= (2x+5)*1/(x^2+5)

[MrApocalypse2012]

@y2kbug77 i know this is old but the derivative of log is 1/x so in this case u are going to have 1/(x^2+5x) x the derivative of the inside which is 2x+5 hope it helps

[iamsmooth]

For the last question y = ln(x^x), since there's already a logarithm, can't you already play with properties instead of taking the natural log of a natural log?

Like y = x ln(x)

y' = x * 1/x + lnx

y' = 1 + lnx

no?

[vrchacho]

You can, cause you can simplify your functions before finding their derivatives. A simplification does not change the values of a function, it gives it's equivalent.

[pimpimbulldog]

No because the function is y=x^x , the ln is introduced by you the differentiate it more easy , and you logarithmatize both of the members including the left side.

[baroqueconcerto3]

you are my fcking hero. thanks!!!!!!!

[lawrencesmallman]

thanks v much, very clear and easy to follow

[pingg317]

first...MASTEROFPUPPETS238 ill like to mention that in denmark we get paid for going to school/university when we are over 18years old (haha).

secound... This guy is a great teacher :)

[xDirectJABx]

WHY CAN'T YOU BE MY PROFESSOR? MINE IS A DUMBASS! Keep up the awesome work man... you`re saving my ass.

[gin012]

sooooooooo proooooo! your vids help me alot

[janitarjanitar]

this guy kicks ass

[bebe2ful]

does he teaches how to do application of Differention??????????? he the only person that makes sense

[MASTEROFPUPPETS238]

and i pay $8K for uni and this guy teaches better

i love you

[finale34]

Your my hero. Please keep these videos awesome and lucid!

[nahumthebest]

Absolutely wonderful :P

[srenhope]

Amazing - keep up the good job.

[ovandocarter]

i swear man i love u

[Kazukiro]

Thanks for explaining this type of differentiation. I've seen equations like these in math competitions and stuff, but I always just memorized the formula. Now I know why that works. Thanks :D!

[memberofslash]

fake

[F00dTube]

baka

[kikilovesuls1314]

thanks! u help me a lot

[trkomando89]

thank you very much for these wonderful videos

[Kakashinoor]

How about 3^x^2?

[bboydjoe]

i got "x(2ln3)*3^x^2"

[bobo441]

hahah,nice.The question where,Y=X^X is the same question I got from my teacher.Throught,ours was to graph it out without our calculator and this video confirms my calculation for that equation.TYTY!!

[Arycke]

For the first example of logarithmic differentiation (5^x), you could alternatively use this formula:

d[a^u]\dx= (ln(a))(a^u)(u')

I use this on problems where you have just numbers as your a, as it saves some time, and it's fairly simple, the derivative is just the natural log of the number (so it's a constant) multiplied to the original function (a^u) multiplied to the power (u).

[YENIQUE1]

In a complex politics question or art, there are so many factors in game and so many strangers that it is very difficult to distinguish the true of the false thing.

The result is that any fool is believed under conditions of discussing on politics and art , while he/she looks at the mathematical one from a respectful distance. (E.SABATO)

[TimeTravelingPizza]

Wow, you make things SO CLEAR. I'm simply amazed. Usually sitting and listening to my teacher talk about these things I don't understand a thing...

But hearing you explain it makes it crystal clear! I didn't know math could be like this!

There might be hope for me this semester!

Thanks!

[azamstat]

Thanks. Good Work.

[zep4life]

Math is one of those things you need to really see it done to understand it, IMO.thanks!

[leviathan6144]

thnx for the up

[TheGreatGoolash]

test tomorrow and I'm sick of reading....this is so cool to have a video!!! Thank you, MathTV!

[Stephendenham]

Of course! So simple now :)

[JujuBeansxD]

OMG THANK YOU!!....this really cleared the fog i had on log differentiation!

[ftothered]

This was so helpful, along with the rest of the videos! They have really put my mind at ease over some upcoming exams. Thanks!

[luvzoya]

someone help me with life and calculus... thank you

[jacobbis4lovers]

Calculus is the math of satan.

[scribbledskiexx]

You said it[:

[recon455]

Calculus is the math of artists and gods.

[nickistheman12345]

and Satan

[jacobbis4lovers]

and satan.

[JonathonRedley]

Ignore the rest of the heathens who decry Calculus as Satan's work.

Try being an engineer without Calculus! :-O

[luvzoya]

im struggling with this calculus every time before i hoped to get an A i ended up with a C... i need to get better grades at this.... thank you your videos make me feel better..hopefully i'll get better at this cause i have a test tomorrow

[jacobbis4lovers]

How did your test go?

[brightnessQQ]

wait i don't get the second step.. can you explain it more clearly ::) thanks!

[huzlar]

could you use Dxe^u = e^u*Dxu for 5^x???? Thanx, youre tutoring was great! this video really helped me, thank you.

[masterjim2007]

are u sure the last method of differentiating is right or in other words can u use just the product rule like the professor did or a mixture of product and chain rule

[Ren520]

coool! very edifying =]] can you do more videos on calculus lol... im gonna be taking ap calc BC exam this may, so i might need help =P

Thanks! i like ur videos!

[seinfan9]

6:06, funny comment

You're a great professor, btw. I can easily understand this.

[huzlar]

can you work some problems from CALC 1 consisting of incrementation and differentiation PLEEEAAAAAAAASEE!!

[tAgRiNa16]

This is excellent review for my Calc exam I have tomorrow!! Thank you!!

[2008151]

thank you thank you thank you

[cutegual]

AN Awesome professor!

[ignuz]

Ok 13 weeks of calc at uni and I am going to fail.. Unless..

1. I study like never before and hope for a pass

2. I find someone who looks like me and knows calc to sit my exam

3. I get hypnotised into learning calculus..

[deanis15]

i can keep calc fresh in mind during the summer

[sjsawyer]

You forgot to close your bracket near the end of differentiating that last function!

Then again who the hell cares because your teaching is superb!

[bluedragon62]

Thank you very much for doing this, you are an excellent teacher. This is something I thought was beyond me, but when you explained it, it really is quite a simple process.

[tomdamho]

WOW very good stuff...i learned a couple of things i didnt know just wish i didnt have my calc midterm last week i think i messed up o well i know it now ...thank you

[silycaon]

i have a calculus exam on thursday :( i feel for you!

[vankalman]

keep up the great videos, you're helping out alot of people and making math fun at the same time! Thanks

[nullifiedmindz]

omg...my professor is leigh becker...he friggin does research using differential equations(even wrote the book we will use for Differentials)...hes not a bad teacher...wish hed do an amazing video like this..i learned logarithmic differentiation and i learned a bit about implicit that i hadnt yet fully understood...THANK YOU

[Grundalizer]

This guy is an AWESOME teacher. He points everything out and makes sure to tell us how he is getting his answers. Excellent job. My high school should just replace my calc teacher with a video screen with this guy on it.

[AboodiX]

one of the best teachers i'v ever seen..

THANKS!!!

[reubentexidor]

My professor is a bold mumbling idiot who doesn't care if we learn...at least your not...your still bold though :)

[XedLos]

THX a lot keep up the good work

[bkjoelover]

man he's so hot right now/

[luvonjpeezy]

Wow, perfect free tutor. God bless you!!

[grenePnaimoskee2]

I wish you were my professor. I think I'm going to fail Math 251, because my professor just stands there deriving formulas and mumbling to himself. This helps a lot though.

[kantana1022]

I LOVE MATH!!!!

[deathwishtomax]

that helped alot.. ur good.. plus you write neat, my teacher writes like a nincompoop.

[LTF85199]

this guy is the beeeeeeeeesssssssssssst

thank you sooooooo much!

[TrueToHeart]

love it!! XD

[jamesharrison1991]

'Hey who made this

[k0tiak]

this guy is a beast

[stevieola33]

hahaha. that was the funniest and the most enjoyable lecture i've ever heard!!! KEEP IT UP!!!!

[farhannius]

man he's so clever

[bkjoelover]

nice shirt professor!

[Hiroyuki665]

WOW

[32docholiday]

GREAATT KEEP THE CALCULUS COMING!!

[Wilkystyle]

Excellent videos! They have helped me many times.

[danielmenendz]

GREAT JOB!!!!!!!!

[Iwanthax]

this guy is one of the best calculus teachers ever!