Derivatives of Polynomial Functions: Power Rule, Product Rule, and Quotient Rule

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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.

[@marekjanik9962]

Power Rule @0:58 Sum Rule @3:35 Product Rule @5:35 Quotient Rule @8:37

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So far this playlist has been amazing! I'm looking forward to watching the rest.

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Man, your calculus playlist is the friggin best! Thank you sm

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Bro i know it's only the starting of Calculus, but it turned out way simple and sophisticated than I'd expected.

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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

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Varsity professor; takes a month me; still confused prof Dave; 12 minutes me; ooooooooooooooooohhhhhhhh

[@jugalpokar]

You made it so easy for me to learn calculas Thanks !

[@pfever]

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

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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.

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[@avjeet888]

better than my teacher

[@sabrinaartist7269]

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

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you're my hero prof dave

[@robertplatt643]

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.

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✨Thank you, Sir, 🙏🌺✨

[@ddevil768]

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.

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[@drvir]

1st comment Hi Professor! You helped me top my chemistry exam

[@bartonpaullevenson3427]

The "up next" function in KZbin 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.

[@ProfessorDaveExplains]

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.

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@@ProfessorDaveExplains Thanks!

[@AlexanderSchwarz-ck3cx]

They told me this will be hard but damn its fun and thanks to your explaining skills I instantly got it right!

[@ivan_ivan0v_]

Thank you for the useful video!

[@matiasrafaelaltamiranda8689]

10:08 can we cancel the x² + 4x?

[@Alex-02]

No

[@johnsolly]

There's a typo at 10:30. There should be dots between the letters in the quotient rule to indicate multiplication.

[@ProfessorDaveExplains]

When the symbols are just next to each other it still indicates multiplication

[@johnsolly]

@@ProfessorDaveExplains agreed! I’m mainly pointing out that it is following a different format than the rest of the equations on the same page.

[@riemanngeometry9266]

Can you derive these derivatives rules

[@ProfessorDaveExplains]

the power rule was derived in the previous clip!

[@riemanngeometry9266]

No, i mean product or quotient rule

[@csmrfx]

This is the good schtuf!

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Prof Dave I will never doubt your big 🧠.🙏

[@mikejackson6104]

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?

[@ProfessorDaveExplains]

nah the second term will be 16x^2 so you subtract to get -8x^2

[@ash_phoenix3282]

I made the same calculation error the first time, but yeah it would be -(4x+1)(4x)= -16x^2 -4x

[@aerosmith4119]

How expand the denominator at 10.05min , Can some one explained to me? Thanks you.

[@tGoldenPhoenix]

Done.

[@patatatatatata]

TYSM

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Jesus started helping you your homeworks

[@throwawayuser9931]

Thanks a lot

[@thk2005]

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

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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.

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I just started watch this playlist whole just to know the whole maths seems like I started to like maths 😂😅

[@Thaumius]

Whens the annoying chain rule going to be posted?

[@harshsinghal4342]

Well, it isn't annoying at all. It is neat compared to the rest of the calculus.

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I just completed 103 videos

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I wrote it.

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just dis this in maths

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[@Jason-ft5xm]

Power Rule @0:58 Sum Rule @3:35 Product Rule @5:35 Quotient Rule @8:37