Derivatives of inverse functions | Advanced derivatives | AP Calculus AB | Khan Academy
HTML-код
- Опубликовано: 6 сен 2024
- Courses on Khan Academy are always 100% free. Start practicing-and saving your progress-now: www.khanacadem...
Functions f and g are inverses if f(g(x))=x=g(f(x)). For every pair of such functions, the derivatives f' and g' have a special relationship. Learn about this relationship and see how it applies to __ and ln(x) (which are inverse functions!).
Watch the next lesson: www.khanacadem...
Missed the previous lesson? www.khanacadem...
AP Calculus AB on Khan Academy: Bill Scott uses Khan Academy to teach AP Calculus at Phillips Academy in Andover, Massachusetts, and heÕs part of the teaching team that helped develop Khan AcademyÕs AP lessons. Phillips Academy was one of the first schools to teach AP nearly 60 years ago.
About Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything.
For free. For everyone. Forever. #YouCanLearnAnything
Subscribe to Khan AcademyÕs AP Calculus AB channel: / channel
Subscribe to Khan Academy: www.youtube.co...
i love how i have a derivative test tomorrow and inverse functions STILL confuse me
update: four days after my calc test and i figured it out yay !
@@xox0babe love that for u :')
this is me RIGHT NOW
@@wesleylai2895 good luck!!
@@xox0babe What you get on the test tho?
There is a much better way to think of the derivative of the inverse function: don't put the derivative of the inverse in the denominator. That is the derivative you want to find out, so why would anyone put it in a denominator?
You get this:
g'(f(x)) = 1/f'(x).
But then you have to remember that f(x) is just equal to y. So f(x) = y. Then you can just simplify as g'(y) = 1/f'(x).
Great coment. Thank you, mate!
Agreed that we are looking for g' and not f'. IMO the best way to find g' based on knowledge of f' is the following: f(g(x)) = x --> f'(g(x))*g'(x) = 1 --> g'(x) = 1 / f'(g(x)). Example: d ln(x) / dx = 1 / e^(ln(x)) = 1 / x, where e^(ln(x)) is the derivative of e^x at ln(x). To be fair, Sal kind of hints at this at the end, but should be explained explicitly in lieu of the other direction that he did explain.
Thank you!!!
Last minute review at 3 am before my midterm 😭
Impress with the clean and easiness of this trick. really easier than calculating about limit to get derivatives .
stan khan academy guy for clear skin
Pov: you are studying Calc. and forgot about algebra & pre.
Complexity persists if finding inverse of a function is tough
I'm still stuck on the chain rule concept, shown again here. We've learned previously that the notation d/dx [g(x)] is the same as g'(x). So here, we see that d/dx [g(f(x)] is actually g'(f(x))*f'(x). So, d/dx (g(x) should simultaneously be g'(f(x)) AND g'(f(x))*f'(x). I get that somehow the phrase 'with respect to...' plays a part here, but in this video, there's no indication that g'(f(x)) is 'with respect to' anything in particular. If someone could help me with this, I feel like it's all downhill from here!
You know its a quality content if its Khan Academy😃💙
damn,I spent an hour on my textbook trying to understand this concept and I couldn't get it. And your video just helped me understand it in 2 minutes lol. Thank you!
Thank you from Bangladesh.....
2:16
The derivative of a function and the derivative of its inverse are related
Yes, original function is rise/run and its inverse is run/rise. So just take reciprocal of derivative of corresponding point
Great video but it really confused me when they found the derivative of f(x) instead of g(x) which is the inverse of f(x), but it's basically the same thing anyways.
Make a lot of videos on permutations and combinations
Great video!
g(f(x)) isn't equal to 1 cuz we can write it as g(x) o g-1(x) and isn't this equal to 1 am i remember wrong?
what program does he use to do this?
3rd! lol the comments on khan academy is much better than the youtube comments
please make a video on Lean Six Sigma
nice
neat
When you unironically say "the number E"
I trust in Khan Academy 🎊☑
By any chance is there a video discussing Constant Of Proportionality? I need it.....
SeriesKJ i don't think there's enough to say about it to make a video honestly; there's just one thing x proportional to y mean x= c * y and c is your constant or proportionality if you know x and y it's basic algebra to find c (spoiler x/y = c)
Make videos on circular permutations
Wow
será traduzido para português ?
Cristhian Lucas no hasta ahora
Translation
Ronaldo Ronaldo RONALDOOOOOO
GOOLLL GOL GOL GOL GOOAAALLL!!!!
!!!!
the inverse of e^x is actually just e^x..
Nope it's log x
ur going too fast
Yo
1st