I know this channel for many things besides math, but your calculus videos are underrated. The pace, the visuals, and the fact you stop to prove things are so effective.
It is easier to memorize if you arrange the terms in product rule and quotient rule as follows: Product rule: ( f * g )' = f' * g + f * g' Quotient rule: (f / g)' = (f' * g - f * g' ) / g^2
I really love how this guy is able to explain things in a very understandable manner unlike some other popular yt channel out there that just jumps right to giving examples not really clarifying the outline of the subject leading us to fail in assessing the situation
When you have a product (f*g)‘ and you multiply it as in your examples and you takw the derivative of that it actually is the same as the product rule, isnt it? For example: (3x^4)*(5x^2) is equal to 15x^6. Taking now the power rule we have 5*6x^6-1 = 90x^5, which is the same result you got with the product rule. Sorry if i‘m stupid and this is completely wrong
I am having a moment right now... never realized how much the educational program in my school sucked until I stumbled upon your videos. We were simply told that this thing must be equal to that thing with no further explanations. Wish I had your videos back when I was still in school.
I find it interesting that the quotient rule isn’t so much a rule as it is a shortcut since I was able to do (x^2 + 1) / (x + 2) using the product rule instead since division is just multiplying by a fraction so (x^2 + 1) * (x+2)^-1 with the product rule got me the exact same result.
The "up next" function in RUclips is extremely screwed up for these, at least for me. To get the videos in the correct order, I had to do a lot of hunting.
in the future just go to my home page and select the appropriate playlist, everything is organized nicely. for math, i have one gigantic math playlist, as well as smaller playlists for each topic, such as calculus.
The main difficulty for modern humans learning ancient mathematics is those crazy symbols of ancient mathematicians, they are not descriptive, and very difficult, if you have to type from the keyboard, because humans have put paper and pencil aside for some time. Therefore, a set of simple and clear mathematical symbols that can be input from the left to the right with the keyboard is necessary to be invented and become the standard.
love your videos well done (been really helpful to me), for your comprehension check example of the quotient rule don't you get +8x^2 from the first term and - 8x^2 from the second so they cancel out or am I missing something?
Quotient rule 8:37 can be prove by this (f*g)' = (f* (1/g) )' = f' * 1/g + f * (1/g)' = f' / g + f * ( -g'/g^2) = the Quotient rule about (1/g)' , as to the rule of power, 1/g = g^(-1) apply the Power Rule, its derivative is (-1)*g^(-2) = (-1)* (1/g^2) = -1/g^2 and as it is a composite derivative so -g'/g^2 nvm its some facts at later video
Power Rule @0:58
Sum Rule @3:35
Product Rule @5:35
Quotient Rule @8:37
you have no idea how much my maths limited me in doing science. how i can do everything thanks to you :)
I know this channel for many things besides math, but your calculus videos are underrated. The pace, the visuals, and the fact you stop to prove things are so effective.
So far this playlist has been amazing! I'm looking forward to watching the rest.
Man, your calculus playlist is the friggin best! Thank you sm
Bro i know it's only the starting of Calculus, but it turned out way simple and sophisticated than I'd expected.
It is easier to memorize if you arrange the terms in product rule and quotient rule as follows:
Product rule: ( f * g )' = f' * g + f * g'
Quotient rule: (f / g)' = (f' * g - f * g' ) / g^2
I really love how this guy is able to explain things in a very understandable manner unlike some other popular yt channel out there that just jumps right to giving examples not really clarifying the outline of the subject leading us to fail in assessing the situation
I hope you would put exercises for us to practice by the end of every math video :D
there are!
You made it so easy for me to learn calculas
Thanks !
you are just amazing... need more professors like you
Thank you sir for your dedication and for making this free! 🙏
Varsity professor; takes a month
me; still confused
prof Dave; 12 minutes
me; ooooooooooooooooohhhhhhhh
When you have a product (f*g)‘ and you multiply it as in your examples and you takw the derivative of that it actually is the same as the product rule, isnt it? For example: (3x^4)*(5x^2) is equal to 15x^6. Taking now the power rule we have 5*6x^6-1 = 90x^5, which is the same result you got with the product rule. Sorry if i‘m stupid and this is completely wrong
you're my hero prof dave
I am having a moment right now... never realized how much the educational program in my school sucked until I stumbled upon your videos. We were simply told that this thing must be equal to that thing with no further explanations. Wish I had your videos back when I was still in school.
I find it interesting that the quotient rule isn’t so much a rule as it is a shortcut since I was able to do (x^2 + 1) / (x + 2) using the product rule instead since division is just multiplying by a fraction so (x^2 + 1) * (x+2)^-1 with the product rule got me the exact same result.
✨Thank you, Sir, 🙏🌺✨
They told me this will be hard but damn its fun and thanks to your explaining skills I instantly got it right!
better than my teacher
Thank you for the useful video!
Done.
The "up next" function in RUclips is extremely screwed up for these, at least for me. To get the videos in the correct order, I had to do a lot of hunting.
in the future just go to my home page and select the appropriate playlist, everything is organized nicely. for math, i have one gigantic math playlist, as well as smaller playlists for each topic, such as calculus.
@@ProfessorDaveExplains Thanks!
TYSM
Dude you are best man.
Your little bossa nova breaks remind me of when I lived on the beach at Bahia, when I should probably have been learning calculus instead.
1st comment
Hi Professor!
You helped me top my chemistry exam
This is the good schtuf!
The main difficulty for modern humans learning ancient mathematics is those crazy symbols of ancient mathematicians, they are not descriptive, and very difficult, if you have to type from the keyboard, because humans have put paper and pencil aside for some time. Therefore, a set of simple and clear mathematical symbols that can be input from the left to the right with the keyboard is necessary to be invented and become the standard.
Prof Dave I will never doubt your big 🧠.🙏
Thanks a lot
love your videos well done (been really helpful to me), for your comprehension check example of the quotient rule don't you get +8x^2 from the first term and - 8x^2 from the second so they cancel out or am I missing something?
nah the second term will be 16x^2 so you subtract to get -8x^2
I made the same calculation error the first time, but yeah it would be -(4x+1)(4x)= -16x^2 -4x
Can you derive these derivatives rules
the power rule was derived in the previous clip!
No, i mean product or quotient rule
I wrote it.
There's a typo at 10:30. There should be dots between the letters in the quotient rule to indicate multiplication.
When the symbols are just next to each other it still indicates multiplication
@@ProfessorDaveExplains agreed! I’m mainly pointing out that it is following a different format than the rest of the equations on the same page.
Quotient rule 8:37
can be prove by this
(f*g)' = (f* (1/g) )'
= f' * 1/g + f * (1/g)'
= f' / g + f * ( -g'/g^2)
= the Quotient rule
about (1/g)' , as to the rule of power, 1/g = g^(-1)
apply the Power Rule, its derivative is (-1)*g^(-2) = (-1)* (1/g^2) = -1/g^2
and as it is a composite derivative so -g'/g^2
nvm its some facts at later video
Y
How expand the denominator at 10.05min , Can some one explained to me? Thanks you.
Jesus started helping you your homeworks
I just completed 103 videos
I just started watch this playlist whole just to know the whole maths seems like I started to like maths 😂😅
I need the reason, why? Why is that?
Whens the annoying chain rule going to be posted?
Well, it isn't annoying at all. It is neat compared to the rest of the calculus.
ur amazig
10:08 can we cancel the x² + 4x?
No
just dis this in maths
😍
Power Rule @0:58
Sum Rule @3:35
Product Rule @5:35
Quotient Rule @8:37