Calculus - Understanding the chain rule
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- Опубліковано 23 чер 2024
- The chain rule can be one of the most powerful rules in calculus for finding derivatives. Unfortunately the rule looks a bit odd, and its unclear why it works they way it does. This video will cover the idea behind why it works and even show how you can use these ideas to build the triple chain rule. For more videos please visit www.mysecretmathtutor.com
You taught me more in 12 minutes than my teacher taught me in four classes. Thank you so much!!!
roane dekeyzer i
Thank you so much. You're literally the reason why I passed my calculus final exam.
this guy has such a soothing voice to listen too for when i’m having a mental break down over my calculus homework
Hang in there. One day at a time. :^D
Nicely explained!
Something worth mentioning in the video though is why you multiply the derivatives, instead of, say, add or subtract them;
in 2:06 you say it's made of 2 smaller processes and then you just write them next to each other but it's not very clear why multiplication is the right action.
If one of the derivatives is twice as big, then the whole derivative should, too, which makes sense but is not a very trivial argument.
l think it'd be better if you added some note about it, either in the description or as an annotation.
Thanks!
Good point, thanks for the tip. :^D
Thank you! I've been trying to get a more intuitive understanding of this rule because I don't like the blind 'plug and chug' formula thing. I'm still not 100% sure on it, but I feel a lot closer to understanding.
This helped me a lot!! Keep making such beautiful videos! Your patience is so cool when it comes to teaching such complex topics.Thanks a lot buddy!
This makes way more sense. I'm semi-studying for Calc next year and I'm in Honors Algebra II right now. I've seen like 3 videos on the chain rule and they never explain it. They just say it as it is. Thank youuuuu
Wonderful style of explaining maths..i really liked your tutorial...
Thank you so much! This video really helps me understand what the chain rule actually means when finding derivatives. :)
Excellent. Thank you. I've watched a number of chain rule videos, and this is the first time it clicked really for me. I sort of understood it, but didn't feel comfortable. Now it makes sense to me. I had a bit of trouble following the triple, but I'll watch it again and maybe write it out with the f, g, k from the previous part.
Thank you sir for blessing us with knowledge
Thank you, but could you explain to me how you got (f' = 2x) when you are trying to find (h')=4
Thank you sir. I understand now :)
You are brilliant.
Thanks. First time I saw chain rule with 3 things... Now I get it
I keep referring to this video as it makes the chain rule much easier to understand. I now understand the "mechanics" of what is going on. The only confusing aspect is (for example on the first equation) the number 4 is still added to the inner equation which still goes to 3 but we also have the derivative of 2 from the first input so we are using 4 and 2 rather than just one of the numbers
awesome teaching
i need a teacher as you
With regards to my earlier question about where do you get 2x from - I see that you multiplied the exponent by the inside function of "X" or "U" depending upon notation
this makes a while lot of sense now. I was trying to find the d/dx of ln(sinx). Which, going by what this says, spit me out cotx, which is correct. Thanks!
Sir really it is very useful for children thank you
Thanks
Helps
Thank you sir🤩
Thanks so much
At the 4 minute 41 second point of the first working, how does the derivative of F = 2X?
This comes from looking at the outside function f which is equal to x^2.
To get its derivative we use the power rule and arrive at 2x.
At the 3 function example you made a mistake saying g(h(x)) then changed the h to k without saying what you did.
Why not just factorise to give 4x^2 - 20x +25 then differentiate to give 8x - 20 and sub in x=4?
great video! but why do we multiply the two derivaties instead of adding or any other operation?
The multiplication has primarily to do with how the functions are linked to one another. When two functions are combined using composition the output of one becomes the input of the next one. input -> g -> f -> output
So any change that happens in the first function potentially get amplified when it arrives at the second function.
A good "real world" example of this is two gears that are connected. If we double the turning speed of the first gear, the result will multiply the rotation of the second gear accordingly. Derivatives are about keeping track of this rate of change, so with composition we see the derivatives are multiplied.
Hopefully that helps out a bit. :^D
@@MySecretMathTutor ahh i see, it's about maintaining proporotinality within a "closed system" eg two gears. thanks for the explanation!
thaaaaank you so very much for your videos you are probably gonna save me from failling in calculus xD
I have a question that may come up as somehow dumb, but,
Isn't (2x - 5)² the same as (2x - 5) × (2x - 5) .. and just using the product rule is supposed to work it out?
That is correct. I would encourage you to also do it using the product rule to convince you that these rules are consistent with one another. :^D
helpful
At 4 mins 42 secs how did you get the derivative of the outside function of 2 as 2x?
It was power rule, which states that the derivative of a power function is nx^(n-1) if n is the initial power, so x^2 becomes 2x^(2-1). That simplifies to 2x^1 or just 2x.
Mr Eric, is there a way we can donate as a token of our gratitude? This may also help you continue with your good work. Please start a patreon account :)
12:34 why is it multiplied by two , where did the two come from ?
The 1/2 and 4 are multiplied together to get 2.
i was going to give you a thumbs up anyway, but i thought it was cool when it went from 199 to 200. i kinda wasn't paying attention to the 199 but i sure noticed that it was now a nice round 200. i know, i get too excited over simple numbers, but hey, this calculus stuff is too fancy for me.
where'd you get f prime = 2x from my guy
I'm not sure if the explanation of why it works is mathematically rigorous
uhm this really isn't an explanation of why it works... just how with numerated examples :/
Harvey Williams try this use dy/dx and use the intermediate variable z that cancels when thinking of these as fractions (dz/dx)(dy/dz) so what's happening here is ur taking the derivative of the intermediate variable in terms of x multiplied by the derivative of y in terms of z
Harvey Williams so if you had lets say f(g(x)) and you wanted to find the derivative of that you would make z=g(x) and find it like such f'(z)=(f'(z))(z') then replace z with g(x) which we can do because we said z=g(x) so f'(g(x))=(f(g(x)))(g'(x)) apply this to your function and bam u got it
Thanks :) I realised I was actually just looking for a really consise way of explaining why normal differentiation works (rather than taking it as a given in this video)
hiçbişe anlamadım saygılar...
7:35 = Mathception lol