Introduction to Logarithmic Differentiation
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- เผยแพร่เมื่อ 5 ก.ย. 2024
- 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...
_________________________________
Final Exams and Video Playlists:
www.video-tuto...
Full-Length Videos and Worksheets:
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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))
ok Harvard material.
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The funny thing is I understand what you mean 😂
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
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
How was it
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I just found your channel, and it's awesome. This is exactly what I needed. It's not explained in my textbook at all.
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 TH-cam TV with the Organic Chemistry Tutor.
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dude this video saved my LIFE
You forgot the chain rule on ln(lnx)
It has really helped me understand logarithmic differentiation
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!
I’m hoping to never see this again once I’m out of school
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.
You explanation is very clear
4:00 why the derivative of ln y = 1/y*dy/dx? why dy/dx?
I am not sure, but when it comes to the derivative of anything related to y, it should be multiplied by dy/dx.
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).
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Why do we use ln x instead of ln |x|, so there are less restrictions on the f'(x) ?
with absolute value there's gonna be more mess
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
@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.
@@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).
i keep on hearing you say "ellen"
😂😂'Ellen' is 'ln'
This video is so helpful. Thanks you
The Goat
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
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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!
If you needd an explanation, search implicit differentiation!
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
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
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Thank you.
Couldn't you simplify sin(x)/x to 1?
No, this is math, not engineering
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I used the quotient rule and had the same thing. Your New Einstein ayo😂😂😂
Excuse me sir..please how come you got
1- 1nx after using the product rule... I'm a little bit confused
why can't we apply the chain rule for the problem: d/dx [ lnx ] ^ x
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.
th-cam.com/video/8MP6eart_Pc/w-d-xo.html
variables = letter numbers
You're here because you couldn't understand your lecturer, aren't you?
sadly yes
I was not present
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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 :)
Yes that's valid..even, if u use implicit func basic formula that's give the same ans. too
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.
Thanks a lot!!! You are Awesome!!!
For the last one, couldn’t you also answer it as
((1-lnx)/x^2)(x^1/x)?
No
@@lalotothemax Why not?
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Good explanation
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?
Great explanation 🙀
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At the 10:10 why we do not use the quotient rule?
You can use the quotient. It will just end up the same answer.
Dude I’m a meteorology major, why do I need to take calc 2
8:23 wont you need to find the derivative of the base of ln[lnx] making it 1/xlnx 1/x?
Question: y= (sin x)^logcosx^2
if this is on my quiz I'm gonna cry.
The name is ORGANIC TUTOR"...
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At 9:38 why do you choose to take the natural log instead of taking a normal log?
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
Mhhhh u know everything keep on helping us
Thanks for that.
Can anyone explain the lnx in 8:33
At 9:20 I did not get your answer; instead my answer is dy/dx= (ln x)^x [ ln(lnx) + 1/(x ln x). The way I have received this is that the dy/dx [ln (ln x)]× x is (ln x)'/(lnx), then [(x')/(x)/(ln x)]. Next we get 1/x/x/(ln x) or (1/x^2)/(ln x) or 1/(x^2 ln x). Finally one x is got cancelled and we get 1/(x lnx).
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
Can someone explain d/dx(ln(lnx)) is not 1/Inx? Like lny become 1/y. thanks
Why am I always here before my exams???
For the first problem, can't you simplify sin x/x and write it as 1?
Bro you can do that when x is tending to zero.. in limits basically.
Do you have a video that has actual numbers as powers.an getting confused some where
Thank you so much!
6:05 why did you insert another natural logarithm there?
tf u saved my life bruv
Thank you!
is sinx/x = 1?
yes
so is x/sin x
@@karisc.anoruo2212 no there's no possible value for which sin(x)/x = 1, becuase then there would have to be value for which sin(x)=x.
however, the limit as x -> 0 of sin(x)/x = 1, it just never physically reaches there
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Bh is d/dx the same as dy/dx,,this confuses me
No, d/dx means your finding the derivative for it, dy/dx only comes when you try finding a derivative for y
Thanks a lot!
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