Introduction to Logarithmic Differentiation

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This calculus video tutorial provides a basic introduction into logarithmic differentiation. It explains how to find the derivative of functions such as x^x, x^sinx, (lnx)^x, and x^(1/x). You need to take the natural log of both sides of the equation and perform implicit differentiation to find dy/dx. You need to be familar with product rule for derivatives and properties of logarithms.
Derivatives - Fast Review:
• Calculus 1 - Derivatives
Derivatives - The Product Rule - f*g:
• Product Rule For Deriv...
Derivatives - The Quotient Rule:
• Quotient Rule For Deri...
Derivatives - The Chain Rule:
• Chain Rule For Finding...
Derivatives - Composite Functions:
• Derivatives of Composi...
__________________________________
Implicit Differentiation:
• Implicit Differentiation
Derivatives of Inverse Trig Functions:
• Derivatives of Inverse...
Derivatives of Exponential Functions:
• Derivatives of Exponen...
Derivatives of Logarithmic Functions:
• Derivative of Logarith...
Logarithmic Differentiation:
• Introduction to Logari...
___________________________________
Derivatives - Using Logarithms:
• Finding Derivatives Us...
Derivatives of Inverse Functions:
• Derivatives of Inverse...
Derivatives - Differentiation Rules:
• Basic Differentiation ...
Derivatives - Function Notations:
• dy/dx, d/dx, and dy/dt...
Derivatives - The Reciprocal Rule:
• The Reciprocal Rule an...
_________________________________
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Опубликовано:

26 фев 2018

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Комментарии : 209

@TheOrganicChemistryTutor Год назад

Next Video: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-VnB59SrT0PY.html Final Exams and Video Playlists: www.video-tutor.net/

@HamburgerMcBass 3 года назад

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@mathsandsciencechannel 3 года назад

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@23than 3 года назад

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@noimage1254 2 года назад

This dude is literally a godsend. He is singlehandedly helping me pass AP Calc.

@keziab6758 2 года назад

Why am I learning this in regular calc smh

@hsienkangliu1436 Год назад

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@nvsreddy Год назад

Also try Khan academy, he teaches intuitively.

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@@keziab6758 i mean the content is still gonna be the same, AP just moves rlly fast

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@dong-wooklee 2 года назад

Shortcut for derivative of a function of type: f(x) raised to g(x) Let f(x) be f Let g(x) be g Let derivative of f(x) be f' Let derivative of g(x) be g' d/dx(f^g)=(f^g)(f'(g/f)+g' log(f)) For those who couldn't understand what's written above, It reads as: derivative of f raised to power g is equal to f raised to power g times (derivative of f times g by f + derivative of g into log(f))

@rosean374 2 года назад

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@Himself868 2 года назад

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@emmaswan312 3 года назад

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@nutitsjustnut7353 3 года назад

Your a great teacher and a great explainer 🥰 struggle to understand this topic for almost 2 years and you explain just in 13 minutes for me to understand ✨ thank you so much

@por_chae 4 месяца назад

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@georgesadler7830 Год назад

MR. Organic Chemistry Tutor, thank you for an exceptional video/lecture on The Introduction to Logarithmic Differentiation in Calculus Two. There are multiple ways to attack problems of this magnitude in Calculus. This is an error free video/lecture on RU-vid TV with the Organic Chemistry Tutor.

@opz0diac 3 года назад

Love the reassurance at 5:41

@YvonSmart 4 года назад

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@shannontobin7825 3 года назад

Im not even 3 minutes into this video and it had already cleared sp many things up!! Thank you ssooo much. I have an exam this Friday (April 23rd) and this is an important part of the exam

@gnation855 Год назад

How was it

@sunflower01212 3 месяца назад

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@benicia9408 Год назад

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@nanganouskamanchey1769 2 года назад

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@joshuasenteu237 Год назад

It has really helped me understand logarithmic differentiation

@ryanzink9 3 года назад

My teacher accidentally deleted the video of him teaching this and I was gone that day. Saving my life once again!

@andyhuang1505 8 месяцев назад

how is this man so goated at teaching. why is this guy not a university prof.

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@shawnfernandez1077 4 года назад

You explanation is very clear

@selenide5768 2 года назад

i hope i get kidnapped and am asked to calculate the derivative using logarithmic differentiation in order to leave. thanks to this video ill be able to do that.

@jaredjones1752 3 года назад

Once you get out of school, logarithmic differentiation can be used in solving problems that traditionally require the product rule or the quotient rule. Less formulas to memorize!

@charlie_nolan 2 года назад

I’m hoping to never see this again once I’m out of school

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@werawkthishousedown 5 лет назад

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@jericcenon6782 4 года назад

You forgot the chain rule on ln(lnx)

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@Dytalks 9 месяцев назад

I dont understand why (me) Computer application student learn these maths 😢what was the point ?

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@LoadBearingSolder 4 года назад

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@rosette_renah 3 года назад

😂😂'Ellen' is 'ln'

@nicholasguagliano1947 8 месяцев назад

The Goat

@shadrickngosa5297 Год назад

Good explanation

@migzwrld909 3 года назад

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@thatomofolo452 Месяц назад

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@user-mm2bf6nt6i 8 месяцев назад

Thanks a lot

@nikedimazn3872 6 лет назад

In the 3rd example, shouldn't the variable exponent go inside the parenthesis, and then bring it down in the parenthesis of the outside most ln

@sinalosanele6562 6 лет назад

awesome

@CrispyCroustillant 8 месяцев назад

your videos really saved me from nonsense classes and dying midterms...

@gabrielcoimbra5850 Год назад

5:54 can I take take the derivative of [ln x^x] like 1/x^x × derivative of x^x?

@onyx9693 Год назад

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@omadasamuel7406 3 года назад

Excuse me sir..please how come you got 1- 1nx after using the product rule... I'm a little bit confused

@Vijay_helo 2 года назад

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@kienanmoodley3521 Год назад

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@lawofselfcontrol 3 года назад

4:00 why the derivative of ln y = 1/y*dy/dx? why dy/dx?

@iNullFlag 3 года назад

I am not sure, but when it comes to the derivative of anything related to y, it should be multiplied by dy/dx.

@jcers 2 года назад

Because we have defined y to be a function of x. So, because y is a function, we have to use the chain rule when we differentiate ln(y).

@saklinsk4618 3 года назад

Thank you sir. :)) . .. ...

@lam7por962 3 года назад

Anyone can please answer me, at 1:06 , when taking derivatives of ln y, why 1/y has to be further multiplied by dy/dx? whats the use of the dy/dx here? Any difference if we just keep 1/y? Thankyou!

@zooanimal7578 3 года назад

If you needd an explanation, search implicit differentiation!

@Altair4611 2 года назад

you are applying d/dx to y, if it was d/dx to x then it would just be 1/x if you apply d/dx to anything other than x you have to tag a d(variable)/dx to the end dy/dx is saying the derivative of y with respect to x

@Arthur-so2cd 2 года назад

since y=f(x), ln(y) is the same as ln(f(x)), so it's a compound function and we need to use the chain rule. the derivative of ln(y) is 1/y and the derivative of y is dy/dx

@user-rl4ef7fu7t Год назад

you are too goooooooood

@sa758 5 месяцев назад

for the second question, can't we just take the x to the front? cuz that's an ln property? 6:00 and that gives us x(1/x) which is one?

@fredartson 3 месяца назад

Hey,in the first example where he showed d/dx(x^x), isn't Ln x a transcendental function? Then why can we take the derivative of both sides

@aleksandarristoski2777 Год назад

I have a question. At 8:17 you use the natural log derivative formula and use u'/u to get 1/x ln x . But I used the chain rule formula f(g(x)) = f ' (g(x)) ⋅ g'(x) and got the same answer. Is this valid? Thank you :)

@shachisharma8908 Год назад

Yes that's valid..even, if u use implicit func basic formula that's give the same ans. too

@jbonceu2457 Год назад

To be honest you don't need to add the u' in every derivative techniques as long as you understand how composition of function works, where in theory every techniques then actually uses the chain rule.

@metawhirl4609 3 года назад

Question: y= (sin x)^logcosx^2

@fromblonmenchaves6161 2 года назад

Why do we use ln x instead of ln |x|, so there are less restrictions on the f'(x) ?

@user-he6hn9on1s Год назад

with absolute value there's gonna be more mess

@esma4379 2 года назад

if this is on my quiz I'm gonna cry.

@SquatSimp 3 года назад

Great video, but why do you have to take the natural log at 6:14? Why can't you just bring down the exponent immediately?? Any response would be greatly appreciated

@SquatSimp 2 года назад

@Giorno Giovanna I see, but my confusion is coming from why you can't bring down the exponent as is ln(x)^x --> xln(x) instead of the procedure shown in the video.

@EpicMathTime 2 года назад

@@SquatSimp Well, to answer that question, I have to ask you one first: why do you think you _can_ do that? If it said ln(x^x), you'd be correct, that can be written as xln(x). But it *doesn't* say that, it says ln(x)^x, which has nothing at all to do with xln(x).

@zaynabb.5140 3 года назад

Anyone watching these vids in 2021?

@paranoidowl3798 5 лет назад

At the 10:10 why we do not use the quotient rule?

@justabunga1 4 года назад

You can use the quotient. It will just end up the same answer.

@lostdanielfound9724 4 года назад

why can't we apply the chain rule for the problem: d/dx [ lnx ] ^ x

@justabunga1 4 года назад

If you want to see how to make things clear, you can rewrite (ln(x))^x using base e as (e^ln(ln(x)))^x=e^(xln(ln(x))). Then, differentiate using chain and product rule. You would end up as e^(xln(ln(x)))(x(1/(xln(x)))+ln(ln(x))))=(ln(x))^x(1/ln(x)+ln(ln(x))), which is the same answer as before.

@mathsandsciencechannel 3 года назад

ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-8MP6eart_Pc.html

@abdulahiibrahim552 Год назад

savior

@tuetran8652 8 месяцев назад

Can someone explain d/dx(ln(lnx)) is not 1/Inx? Like lny become 1/y. thanks

@tegetegerobinson5728 Год назад

Why am I always here before my exams???

@diegoarturoortegagrajales8188 7 месяцев назад

6:05 why did you insert another natural logarithm there?

@Ruben-ho9jd Год назад

At 9:38 why do you choose to take the natural log instead of taking a normal log?

@arugula517 Год назад

The derivative of ln is simpler than the derivative of other logs but you could use any log base you want and get an equivalent answer

@ethanwood2397 2 года назад

Bro you gotta turn the sound way up on this I’m on the bus rn on my way to first period where I have a test and I can barely hear shit even at max volume

@avanith3579 3 года назад

Couldn't you simplify sin(x)/x to 1?

@jcers 2 года назад

No, this is math, not engineering

@arnmandleg 3 года назад

variables = letter numbers

@gnation855 Год назад

Can anyone explain the lnx in 8:33

@user-hv6ef9ie1g 3 месяца назад

Nice

@mechanicalkiller1061 5 лет назад

Wonderful explanation #Kfupm FRESHMAN Student Nov2018

@7arigi Год назад

now?

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@big_esh 2 года назад

I love ur voice!! N

@butchifly 5 лет назад

Why does it have to be ln to get the derivative of x raise to x? Why not use log?

@koogalboogal1238 5 лет назад

You could theoretically use log in base b, but that would end up in a much hairier expression than if you were to just use the natural logarithm. Because d/dx(ln(x)) = 1/x. But d/dx(log_b(x)) = 1/(xln(b)) which you can imagine overcomplicates things, which you should try to avoid in problems with expressions that can get hairy enoughas it is.

@justabunga1 4 года назад

The log and ln is denoted differently. log without a subscript means log base 10 or common log. ln stands for natural logarithm or log base e. People tend to confuse with these two just because of the way they like to define. To me, I would go with ln since it will always be used in calculus course. log base something is rarely used.

@justabunga1 4 года назад

There is a way you can do without log differentiation. Change the variable in the base to base e. For example, x^x=(e^ln(x))^x=e^(xln(x)). Then, differentiate using the chain rule and product rule. You will end up the same answer as before.

@rosette_renah 3 года назад

Though both log base 10 and ln are natural logs,, ln is common in calculus, and a bit easier to use