Derivatives - Formula Sheet: bit.ly/4dThzf1 Final Exams and Video Playlists: www.video-tutor.net/ Full-Length Videos & Worksheets: www.patreon.com/MathScienceTutor/collections Next Video: ruclips.net/video/KbYW9FDm-Zk/видео.html
I've spent days trying to get my brain to understand implicit differentiation. After dozens of videos from class and other youtubers, yours is the first one to have it make sense to me. Thank you so much!
thankyou for these videos. I always laugh a little when i pause the video to, for example "divide both sides by sin(xy)^2" then reusme the video and hear "you know what nevermind"
I've watched dozens of videos over the past few months and they have helped tremendously. College algebra to differential calculus; this channel has a LOT of videos that cover very specific topics in mathematics, similar videos are very hard to find. This channel has been a really helpful resource for me since I started going back to school and taking math courses. 100/10 would recommend.
Just wanna say a big thank you to whoever is running this account i had a test earlier today that I've been dreading for days and math is my worse subject, but I watched your videos and you explain it better than my teacher ever did. ill definitely be back for other topics !!!!
I pay tons of money for a professor to ramble nonsense just for me to watch a youtube video myself to pass exams and get a degree for IT, this guy is goated for all his videos
MR. Organic Chemistry Tutor, thank you for an excellent video/lecture on the classical Implicit Differentiation in Calculus I/II. This is an important topic in Mathematics and Engineering. This is an error free video/lecture on RUclips TV with the Organic Chemistry Tutor.
Shortcut for implicit differentiation Take all the things on one side then do as below: dy/dx= -(diffentiate wrt x, take y as a constant)/(differentiate wrt y, take x as a constant) Eg. Lets say I need to differentiate x³+3xy=y²+1 Step1 (taking everything on one side) x³+3xy-y²-1=0 Step2 differentiate x³+3xy-y²-1 wrt x and take y as a constant That would be equal to 3x²+3y Let 3x²+3y = m Step3 differentiate x³+3xy-y²-1 wrt y and take x as a constant That would be equal to 3x-2y Let 3x -2y = n Step4 Apply the rule and obtain dy/dx dy/dx = -m/n = -3x²-3y/3x-2y This may look like this is quite lengthy but in actual it hardly takes 10secs. I wrote this long so that anyone who sees this could clearly make sense of it and understand
Every time I watch one of your videos I'm reminded of Andy Samberg's Mark Whalberg impression on SNL, where he walks around and tells animals "say hi to your mother for me."
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12:56 To add, notice that y³ + x³ is also equal to our original given/expression x³ + y³, and it states that it is equal to 9. So subtituting the value of that expression will yield to a same answer. This is the beauty of second derivate in implicit, original expression tends to have a relationship on some part of it.
@@nokuthulamakhunga7039 Actually, there are times that a given will not give you coordinates like (1,2) etc. But always remember that in implicit differentiation - second derivative, there's a higher chance that your solution will consist of the original given equation like for example here was x³ + y³ = 9, only the majority though, because some are not. Sometimes, you have to make little algebra tricks to make show of the original expression. For example, instead of getting y³ + x³, you get -y³ - x³, what you're going to here is to multiple it by "-" or -1, so it will become -(y³+x³) which will be equal to -(9) = -9.
No, dy/dx doesn't mean that (-8) = dy and 6 = dx. dy/dx just means "derivative of the equation." More precisely, it is "the change in y at any given moment / the change in x at any given moment" which wouldn't be equivalent to x / y. Just plug in the point (6, 8) where x = 6 and y = 8 since point notation is (x, y).
particularly when you distributed it to the derivated of xy^2. I don't see how the x ended up in the derivative of 1y^2, instead of it being 2y, or what happened to the 2y where it's x(2y(dy/dx))
As I understood it now, implicit differentiation is simply derivation with extra precision to what we are differentiating in respect of what. dy/dx. dr/dt. dv/dt ...etc. But normally d/dx is d to respect of X assumed and does not follow the rest of calculation.
Yeah I think it attempts to relate y and x even though they’re visibly (in the equation) not in the regular y = x form. I keep hearing that it applies the chain rule, but if that were the case, then we’d need to treat y not as a single variable but as y(x) or a function of x. (Chain rule in y(x) 👉 would be y’(x) • x’.)
How am I supposed to find the slope of a point when the derivative function (dy/dx) clears out the x input? For example, derivative of 2x - y + y^3 = 0. dy/dx = 2/(1-3y^2). Nowhere to plug in x.
Derivatives - Formula Sheet: bit.ly/4dThzf1
Final Exams and Video Playlists: www.video-tutor.net/
Full-Length Videos & Worksheets: www.patreon.com/MathScienceTutor/collections
Next Video: ruclips.net/video/KbYW9FDm-Zk/видео.html
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I've spent days trying to get my brain to understand implicit differentiation. After dozens of videos from class and other youtubers, yours is the first one to have it make sense to me. Thank you so much!
why can't my professor sound this simple........ anyways luv u organic chem tutor guy
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Because he is way older
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thankyou for these videos. I always laugh a little when i pause the video to, for example "divide both sides by sin(xy)^2" then reusme the video and hear "you know what nevermind"
You're probably the best teacher for any topic I find you teaching. Explain things better than my professors
I've watched dozens of videos over the past few months and they have helped tremendously. College algebra to differential calculus; this channel has a LOT of videos that cover very specific topics in mathematics, similar videos are very hard to find. This channel has been a really helpful resource for me since I started going back to school and taking math courses. 100/10 would recommend.
hes got chem and physics too, perfect for engineering students, bros been boosting my gpa
Just wanna say a big thank you to whoever is running this account i had a test earlier today that I've been dreading for days and math is my worse subject, but I watched your videos and you explain it better than my teacher ever did. ill definitely be back for other topics !!!!
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I pay tons of money for a professor to ramble nonsense just for me to watch a youtube video myself to pass exams and get a degree for IT, this guy is goated for all his videos
You are really making chemistry, physics and maths easy for me.Excellent.
13:35 I believe you could have substituted 9 in for (y^3 + x^3) as well, thank you for the help!
MR. Organic Chemistry Tutor, thank you for an excellent video/lecture on the classical Implicit Differentiation in Calculus I/II. This is an important topic in Mathematics and Engineering. This is an error free video/lecture on RUclips TV with the Organic Chemistry Tutor.
All your videos about calculus is making it easier for me to work on them in uni. Thank you, keep it up 💯
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Shortcut for implicit differentiation
Take all the things on one side
then do as below:
dy/dx= -(diffentiate wrt x, take y as a constant)/(differentiate wrt y, take x as a constant)
Eg. Lets say I need to differentiate x³+3xy=y²+1
Step1
(taking everything on one side)
x³+3xy-y²-1=0
Step2
differentiate x³+3xy-y²-1 wrt x and take y as a constant
That would be equal to 3x²+3y
Let 3x²+3y = m
Step3
differentiate x³+3xy-y²-1 wrt y and take x as a constant
That would be equal to 3x-2y
Let 3x -2y = n
Step4
Apply the rule and obtain dy/dx
dy/dx = -m/n = -3x²-3y/3x-2y
This may look like this is quite lengthy but in actual it hardly takes 10secs. I wrote this long so that anyone who sees this could clearly make sense of it and understand
Interesting method, thanks.
Thank you sir may I ask you a question
7:23 how did -2x=cos xy² become y²cos xy² ??? Where did y² came from ???
@@Maroofgilani621 he distributed cos(xy^2)
@@Maroofgilani621 Chain rule : d/dx sin(u) where u = xy^2
d/dx (sinu) = d/du (sin u). du/dx
d/du (sin u) = cosu
du/dx = y^2 + x.2y.dy/dx
Then cos(xy^2) . (y^2 + x.2y.dy/dx)
wow much love from uganda thanks for simpifying implicit differentiation for me
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ruclips.net/video/Zuh5EiW0o7w/видео.html
Every time I watch one of your videos I'm reminded of Andy Samberg's Mark Whalberg impression on SNL, where he walks around and tells animals "say hi to your mother for me."
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It's so gooood, realizing that d/dx y^3 = d/dx * y^3/dy * dy = d/dx * 3y^2 * dy = 3y^2 dy/dx made my day
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How do you know which terms have the dy/dx?
whenever you differentiate y
12:56 To add, notice that y³ + x³ is also equal to our original given/expression x³ + y³, and it states that it is equal to 9. So subtituting the value of that expression will yield to a same answer. This is the beauty of second derivate in implicit, original expression tends to have a relationship on some part of it.
I have a question,so you mean second derivative will always give you the answer of the original equation if you substitute???
@@nokuthulamakhunga7039 Actually, there are times that a given will not give you coordinates like (1,2) etc. But always remember that in implicit differentiation - second derivative, there's a higher chance that your solution will consist of the original given equation like for example here was x³ + y³ = 9, only the majority though, because some are not. Sometimes, you have to make little algebra tricks to make show of the original expression. For example, instead of getting y³ + x³, you get -y³ - x³, what you're going to here is to multiple it by "-" or -1, so it will become -(y³+x³) which will be equal to -(9) = -9.
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The thumbnail scared me with the -x^2/y^2 i thought everything i knew about derivatives was wrong lol
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Does anyone understand why you add the (dy/dx) and how to know when to add it? I'm confused, how do you know when to put the extra differentiation
You add it when differentiation y variables
You put it on every variable except x
Because dx/dx cancels itself out
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at 2:14 would'nt it be -8/6 because it is dy/dx ?
No, dy/dx doesn't mean that (-8) = dy and 6 = dx. dy/dx just means "derivative of the equation." More precisely, it is "the change in y at any given moment / the change in x at any given moment" which wouldn't be equivalent to x / y. Just plug in the point (6, 8) where x = 6 and y = 8 since point notation is (x, y).
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I was totally following until you changed from dividing to distributing at abouit 6:48. I didn't track how the distribution worked.
particularly when you distributed it to the derivated of xy^2. I don't see how the x ended up in the derivative of 1y^2, instead of it being 2y, or what happened to the 2y where it's x(2y(dy/dx))
at 8:24 , could we cross cos(xy^2) in both numerator and denominator
@toshio3772forgot about that, thanks for clearing it up
7:23 how did -2x=cos xy² become y²cos xy² ??? Where did y² came from ???
He multiples the cos(xy2) into the 1y squared. He also multiples it into the other term that's being added in the parenthesis.
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8:22 , is it considered when you simplify the final answer by expanding it.?
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As I understood it now, implicit differentiation is simply derivation with extra precision to what we are differentiating in respect of what. dy/dx. dr/dt. dv/dt ...etc. But normally d/dx is d to respect of X assumed and does not follow the rest of calculation.
Yeah I think it attempts to relate y and x even though they’re visibly (in the equation) not in the regular y = x form. I keep hearing that it applies the chain rule, but if that were the case, then we’d need to treat y not as a single variable but as y(x) or a function of x. (Chain rule in y(x) 👉 would be y’(x) • x’.)
You have helped me with so so many of your videos, and yet we don't even know your name :(
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How am I supposed to find the slope of a point when the derivative function (dy/dx) clears out the x input? For example, derivative of 2x - y + y^3 = 0. dy/dx = 2/(1-3y^2). Nowhere to plug in x.
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Why do we take the second derivative to find the point on the last problem but not the ones prior?
why you didn't divide by cosine (xy^2) in question 3 ?
once again very helpful
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How does this guy have lessons for all topics