Finding the Derivative of an Inverse Function - Calculus I
HTML-код
- Опубликовано: 15 сен 2024
- 2020 remake with more examples and better video/audio quality:
• Derivative of an Inver...
This video shows students how to find the derivative of an inverse function. I show how to find the appropriate values needed to use the formula for the derivative of the inverse function. If you found this video to be helpful, please LIKE and SUBSCRIBE. If you have any requests, leave the topics you want me to cover in the COMMENT section below. Thanks for watching!
Graduated HS and had him as my Algebra teacher. Now in college and I'm still coming back to him for help.
Hope college is going well, Danny! Good luck with calculus!
I watched so many videos to better understand this concept, and yours was the most clear and concise explanation. Thank you so much!
I am happy you found the video helpful! Thank you for the support.
9 years later, and this is still the most useful video on this topic. So many others focus on how the formula is derived and use a generic function to prove it. That's all well and good, but doesn't come close to helping Calc students understand how to use it and solve HW/test questions. Thank you.
Glad it was helpful! I am so happy to see that my old videos are still going strong. I filmed that video in my room; I had a whiteboard on my wall and a old camcorder set up on a tall armoire.
Hey Vin. There aren't as many video tutorials for this topic and your excellent demonstration saves me from tons of struggle. Thanks a lot :D
Glad it helped! Best wishes with the rest of calculus!
Very clear and wonderful explanation. It seemed very difficult, but with this wonderful explanation it became very clear. Thank you
Glad it was helpful!
This was awesome.!! 😃You managed to talk about a topic involving inverse functions without going back and forth between 'original function' and 'inverse function' multiple times and making it head-spinningly confusing. Congratulations!
Glad it was helpful! How is your calculus class going?
why did it take so long to find you :'( you're my savior
Holy, what an incredible video thank you so much man. I've been looking at this topic now and scrolling through other videos and yours was so much clearer, hope you keep making more videos this was great, thank you!
I appreciate the comment and best wishes with calculus!
Thank you so much!!Ive been trying so hard to understand this concept and youve explained it so clearly!!
I was desperately searching for this and finally got you....... Cleared my all confusions 😊😊♥️
Glad it was helpful!
Wow I love you. I was stuck on a calc problem and google didn’t help one bit but this video did.
Thanks ! The only video I can understand about these inverse functions.
Glad it was helpful!
I SPENT 2 HOURS ON THIS ONE QUESTION, AND YOU OPENED MY EYES @ 3:10
But 0 is not the only solution for f-1(4) as it is a cubic equation it should have 3 solution
Thank you. My calculus book was so confusing. This really helped. If you have the time, please make another video with just the table.
I have an updated version of this video:
ruclips.net/video/l3lXkveIOjY/видео.html
I hope this video helps!
you my friend, are a LIFESAVER. super easy to follow along and understand. thank you!!
dude you're the goat I have been trying so hard to find a video on how to solve for a number when there are multiple terms, now i understand tysm
Best explanation of this. Best video I could find
Glad it was helpful!
This was the best video I could find on this 🙏. Thanks!
Glad it was helpful! I made an updated version of this video, covering a few more examples. Best wishes with calculus and thanks for the sub!
Thank you so much for your nice explanation it was very hard but with your explanation it makes nice 👍 thank you
Hang in there! Calculus is tough at times but keep pushing and you will get through!
Very clear and straightforward, really appreciate the video! :)
Glad you enjoyed it!
literally watching this 2 hours before my midterm and I finally understand now, Thank you!
Glad it helped! Hope your midterm goes well.
Got a Calc B.C. test tomorrow, thanks for this video.
Best of luck!
best video for derivatives of inverse functions
I am glad this old video is still helpful. Good luck with your calc class!
Thank you for this video! Though im kind of confused for this type of question:
Find (f^-1)'(a), if f(x) = x^3 + 2x + 3, and a = 0. Over here I tried applied the concepts of inverse functions where you can say that if f^-1(0) = a. Then f(a) = 0. However, it got me some decimal answer and I had to do some things that I'm not sure are allowed by the professors.
Honestly you could just guess and check because i got (-1,0) on f(x) therefore (f^-1)(0) = -1 and plug that into 1/f’(f^-1(x))
THANK YOU THANK YOU
Great explanation sir, good job! you could not be any clearer litteraly!
you’re acc a life saver 😭 thank you
I am happy to help! Good luck with your class.
Math bless you man, great explanation. Thank you for doing this.
You saved my life
Very clear illustration! Thank you!
Thank you man this helped me a lot bro
Glad I could help! Good luck with the rest of calculus!
Thank you so much
thank you! this was so helpful
Glad it was helpful!
Great job. 👏
OMG this video helped me so much. THANK YOU !
What an explanation 👍👍👍
Glad it was helpful! I hope calculus is going well!
@@vinteachesmath yep
best explanation.
Glad you think so! I updated this video somewhat recently: ruclips.net/video/l3lXkveIOjY/видео.html
Best explanation. Thank you.
Glad it was helpful!
I finally understand this topic thanks a lot(:
Glad it helped!
Forever grateful🤙
Great video. Thanks for the help
Happy to help! Best wishes with calculus!
best explanation son. thanks a lot!
Thank you for the vote of confidence! Best wishes with calculus!
What if there is a trig property in it and an argument like (pi x /2)?
You should not ask rather you should try it on your own...
THANK YOU SOOO MUCH!!!!!!
Happy to help! I am glad my older videos are still going strong!
The best
thank you. Very very simply for me
I am glad it helped! Good luck with your class.
Thank you sir ❤❤
Most welcome!
This was extremely helpful
Thank you!
Welcome! Best wishes with the rest of your semester!
best explanation sir👍👍👍👍
I am glad the video helped!
thnx
that’s amazing
You're welcome!
Thanks a ton Bruh!
Very helpful
Thank you Sir
I am happy to help! Thanks for watching!
Great video, thank you for sharing it.
wait, but is is not 1to1 function. It fails horizontal test, right?
It should be 1:1 since the derivative of f is always positive. Since f' is always positive, f is always increasing and therefore, 1:1.
Correct me please: x² is parabolic function, therefore it cannot pass horizontal test, because there are 2 interceptions
Do you always have to plug in a zero?
No, but it zero is an easy number to try though! Then I try 1, -1, etc. If the numbers get too crazy then you can use a calculator to find out when the function equals a particular value.
So helpful thankyou!
Brilliant👏
Thanks!
Good 🌷
what if the derivative is decreasing? can I still use the formula you used?
As long as it passes the horizontal line test
what is the explanation/rule of the 'we need' box? the derivative of the inverse of the function of x is the inverse of the derivative of the inverse of function x ?
If you want an explanation of the rule, you need to start with f( f^-1(x)) = x (definition of the inverse function). Take the derivative of both sides (Chain Rule on the left) and then divide to solve for the derivative of the inverse function.
Thank you I love you
But there are 3 values of f-1(4) as it is a cubic equation??
thank u teacher for sharing .. it was very helpfulll. but my question is can we just derivate the inverse function normaly just like any normale functio then plug in the 4 number ?
Yes that is an option. However, for many examples they will give you a function where you cannot find the inverse function algebraically.
+vinteachesmath Oh that's what i was looking for . thank 's teacher .
i wish u will do more for us
Love from INDIA
I am happy my videos are reaching people around the world! One of my favorite parts of being a youtuber!
Very helpful.Thanks a lot.
THANKS!
Helpful Thanks
Thanks for watching!
would it not be easier to understand if you just used dy/dx for f prime of x
you got that dog in you fr
I love you.
Ihank you so much👍👍
perfecttttt
Glad it helped! If you want more inverse examples, I have a newer video on this topic:
ruclips.net/video/l3lXkveIOjY/видео.html
Thank you for supporting one of my original videos!
Namaste🙏 sirji💐.
Happy to help!
Very helpful👍
why don't we use the formula g'(y) = 1/f'(x) If f(x) = y the inverse is g(y) = x eg. g( 2x^3 + 3x^2 +7x +4) = x it follows g(4) = 0 so f'(0) = 7 or
g'(4) = 1/7 Cool
uhmm... i got confused. we are talking about INVERSE FUNCTION, it means f(x)=y and we should switch y for x then solve for y to have inverse function, then, we will take f' (y), finally, we will place 4 to the function we got. Is that right?
Yes.. But in cases where the function is difficult to separate, we can make use of this formula.. The formula can be proved by applying the Chain Rule to the definition of the inverse function.
vinteachesmath I see. Thank you very much!
The problem is that it s hard to take the inverse of such functions. What you have to do in those cases is to plug numbers until you find h(x)= the x value you re differentiating the function at... Then consider it as a y value for h(x)-1.
والعباس حجيك معدل زلمه كلف
How did you know to use zero?
Trying out 0, 1, -1 are good numbers to try first because they are easy to plug in. Good luck with your class!
thank youuuuuuuuu
I am happy to help and good luck with calculus!
this is infinite math. to get any accolades from me you have to show this in finite math. F[x]
nice
👌👍
So nice there s no music
I do not have any cool intros to my videos!
i bet your name is mr D you handsome boyy
god bless
💕🥺🥺🥺
help
LmaooooooooooooooooooOOo
very informative vid but youre like distractingly good looking
no homo
Thank you!!
You're welcome!
Thanks so much, this has really helped.
I am glad it helped! I wish you the best with calculus!
god bless