Derivatives of inverse functions | Advanced derivatives | AP Calculus AB | Khan Academy
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- Опубліковано 9 лют 2025
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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!).
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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?
Last minute review at 3 am before my midterm 😭
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!!!
stan khan academy guy for clear skin
Impress with the clean and easiness of this trick. really easier than calculating about limit to get derivatives .
Pov: you are studying Calc. and forgot about algebra & pre.
Thank you from Bangladesh.....
You know its a quality content if its Khan Academy😃💙
Complexity persists if finding inverse of a function is tough
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!
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!
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!
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
3rd! lol the comments on khan academy is much better than the youtube comments
what program does he use to do this?
When you unironically say "the number E"
nice
neat
please make a video on Lean Six Sigma
I trust in Khan Academy 🎊☑
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?
Make videos on circular permutations
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)
Wow
ur going too fast
the inverse of e^x is actually just e^x..
Nope it's log x
será traduzido para português ?
Cristhian Lucas no hasta ahora
Translation
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GOOLLL GOL GOL GOL GOOAAALLL!!!!
Yo
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1st