Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) https://www.patreon.com/patrickjmt !! Derivatives - Product + Chain Rule + Factoring - A quick example for a friend out there in internet land! For more free math videos, check out http://PatrickJMT.com

Text Comments (246)
## Would you like to comment?

Caelin Buenger (2 months ago)

Why do you do the chain rule as well? Wouldn't just the product rule work?

Amir A (1 month ago)

There are most than two functions.

Chief (2 months ago)

I don't understand why you add the second portion of the equation "(4x^3) * (5x-1)^3" "+" "(3) * (x^4) * (5x-1) * (5)" instead of multiplying it? Why the addition sign?

Moises Ramos (2 months ago)

Product rule states the dervative of the first part multiplied by the second part, + derivative of the second part multiplied by the first part.

Marcus Antonius (2 months ago)

WHY MULTIPLY BY FIVE?

Amir A (1 month ago)

take the prime of 5x-1 which is just 5

ADorkNamedSteph (2 months ago)

This helped so much! Thank you!

Kailly’s Channel (2 months ago)

I learned it backwards from my professor because he doesn't teach well. You help me learn so quickly vs the 16 min lectures.

Daniel Alapad (9 months ago)

nice tutorial but your hand is so distructing.

Kathryn Manion (9 months ago)

What, so you said you needed just the 15x to satisfy the extra x term but 15x doesn't belong in a parenthesis like the other xs so why did you do that? Otherwise, thanks for going through the problem!

not mueyzzu (11 months ago)

How did you get 35X ?

TNT BY SM (1 year ago)

This was very helpful, thank uuu!!!

nurul farahaimi (1 year ago)

how u can do it properly clearly

Joaquin Alejandro (1 year ago)

left hand

Niki Mouse (1 year ago)

i've been watching your math videos for my entire high school career! Thank you!!!

kimbellary johnson (1 year ago)

wow u are really helpful!!!

Cinthia Ramos (1 year ago)

So true. OMG. It's the factoring that gets me!

Waheed Saeed (1 year ago)

Neatest handwriting ever

Elizabeth Ponce (1 year ago)

thank you so much for the help!

trwent (1 year ago)

Good Lord, at least get a full-sized piece of paper!! Also, your hands are in the way too much. You should find a way to make those hands invisible.

Effat Hoque (1 year ago)

why u multiply by 5?

野村ERIK (1 year ago)

I think this would be easier with 5x-1 being substituted for another variable/variable prime.

ARIF AZMI (2 years ago)

thanks a lot man!!!
you saved me!

Mike Hunt (2 years ago)

Always forget the second part of the chain rule smh... Thanks man!

Ifraz Ali (2 years ago)

0:46
why you multiply that by 5?

Nicolay Nicolavich (2 years ago)

it is a art of the chain rule man

Case Smien (2 years ago)

why did we put the five at the end

Case Smien (2 years ago)

you multiply by 5 because chain rule is the deriv of the outside x deriv of inside.

Yoel Robaina (2 years ago)

ILY THANK YOU

taizer (2 years ago)

omg thanks finally figured this out after an hour lol

Mario Rodriguez (2 years ago)

Thanks so much for this video!

Asky (2 years ago)

Cheers

John Wu (2 years ago)

Thanks so much bro, you made it much clearer for me😄

numbnuts (2 years ago)

You only explained in depth the simplifying part, not how you used the chain and product rule.

Genesis Layne (2 years ago)

thanks a lot

Cherly (2 years ago)

i dont get it at factorize part. help me

reddgsx (2 years ago)

I wish I could give more likes! Tyvm!

Bob Marly (2 years ago)

THANK YOU LORD JESUS

Jaymon Moran (2 years ago)

You saved me. :)

Nehrose Melgar (2 years ago)

i dont really get it...it might be the hardest part of the math huhuhu

uthman Abubakar (3 years ago)

thanks...

Michelle Quevedo (3 years ago)

OMFG Thank you so much!!! I was stuck on t^9(t4 + 2)^5 on a hw assignment and i kept messing up but your tutorial helped clarify the steps. Thank you!!!

Ricky Desai (3 years ago)

you the real mvp

Maiara Costa (3 years ago)

Damn, will you marry me? LOL

NoMoneyHeadsUp (3 years ago)

Does anybody know why it's PLUS 15x instead of TIMES 15x? (On the second to the last line)

germandrummer13 (3 years ago)

He started with 15x^4, and he pulled out a x^3. He's left with 15x.

aziz as (3 years ago)

Thank you sir

psynostic (3 years ago)

875x^6 - 450x^5 + 75x^4 - 4x^3
These are so fun! :]

firdaus johari (3 years ago)

wasn't 15x suppose to be 15x^3.. where did the power go?

discuss21 (3 years ago)

No see 15x^4 in line 2. Check across brackets, it's still there in line 3 as x^3 multiplied by 15x. You should check the example and factor similar expressions to get more experience.

jonh 866 (4 years ago)

Man u helped me so much

A Cactus (4 years ago)

And my lecturer takes 30minutes to explain a question like this and yet I still don't get it... But thanks to you though :)

Fandy Suryana (4 years ago)

your videos tutoring for those who are struggling with calculus are very useful. Thx for your time putting these videos up for others.

carolina leily (4 years ago)

I really want to know what is in this video to hate?? Thanks a lot, great video

Donna Rayborn (4 years ago)

Thank you, Thank you!! I was so confused and your 3 minute video cleared it up for me!

Aleena Abraham (4 years ago)

You rock, PatrickJMT
Straightforward and easy
:D

Mariah Shepphard (4 years ago)

Frosen. On. Dmann

Jordan Smy (4 years ago)

Nice and Clear! Thank you !

Isabella Mongelli (4 years ago)

THANK YOU U JUST SAVED ME SO MUCH TIME :)))))) !!!!!

Elizabeth Ye (4 years ago)

THANK YOU SO MUCH AHH

Francesco Commisso (4 years ago)

you're writing with the wrong hand

Mark Williams (4 years ago)

wait, where did the 5 come from? At the end of the first step?

Mark Williams (4 years ago)

thank you, lol I have already found that out, but thank you for answering my question :)

Amritpal Chahal (4 years ago)

It's the chain rule. deriving 5x-1=5

ItsVerosLife (4 years ago)

+Torien Worsley its the derivative of the inside part [5x-1]--> 5

TheCireMC (4 years ago)

So helpful! I wasn't understanding the factoring part in equations like that in class.

Elwood Hellsythe (4 years ago)

Why did you multiply by 5 at 0:46

Tabitha Rosa (1 year ago)

ya me too...thanks!

Case Smien (2 years ago)

thanks man! I had the same Q

Mc darryl Atacador (4 years ago)

derivative of 5x-1

Stephon Harris (4 years ago)

Because in the chain rule you multiply the derivative of the outside (in this case d/dx [5x-1]^3 = 3[5x-1]^2) by the derivative of the inside (d/dx 5x-1 = 5) so you should have 3[5x-1]^2*5

Aneesha Kaur (4 years ago)

THANK YOU SO MUCH! literally just saved my life

Nicholas Chua (4 years ago)

Thank you so much!! It took me so long to figure out how to do these questions.

Agon Cecelia (4 years ago)

Do you win more if I watch the full advertisement? If yes let me know, I'll do that all the time to pay you for the great effort and the good job you're doing for us.

Tamen J (4 years ago)

THANK YOU SO MUCH I WAS GETTING SO CONFUSED WITH THE FACTORISING

Akram Adel (5 years ago)

because thats the derivative of the inner part. why, you ask? he's using the chain rule

Ken Lee (5 years ago)

The derivative of (5x + 1) is 5 as (5 multiplied by 1 times x^(1-1) and any number becomes 0.

Ken Lee (5 years ago)

Derivative of (5x + 1) is 5.

s.lena (5 years ago)

so what happened to the 5 in the end of the second line?

ACE2AKA1AMAL (5 years ago)

I fucking love you - no homo. This helped me understand how to clean it up after writing it all out. This helped a lot I was stuck on a question similar to this for like 3 hours... You don't understand omg thanks sooooooo much, liked and subscribe. Great vid keep it up bud. :D

Kevin Topper (5 years ago)

dy/dx (5x-1) = 5

harashe1000 (5 years ago)

Sorry, it's supposed to be -1 not -10! But the concept will still be the same. I hope that helped. :)

harashe1000 (5 years ago)

(5x-10)^3 is a composition of two functions. One is x^3 and the other is 5x-10. When using the chain rule, you take the derivative of the outside function (in this case x^3) and leave the inside alone; so you get 3(5x-10)^2. Then you multiply it by the derivative of the inside function (in this case 5x-10), which is 5. So you get 3(5x-10)^2 multiplied by 5.

Michael O'Connor (5 years ago)

Why is the second part of the product/chain rule multiplied by 5 at the end?

Heman Lu (5 years ago)

its part of the chain rule where you have to multiple the derivative of the term inside the bracket which is 5x-1. The derivative is therefore 5 and you multiply

Amber Hardy (5 years ago)

He took the derivative of (5x-1)^3 and then he took the derivative of the inside of the parenthesis, which is 5x-1. The derivative of this is 5. In other words, he used the chain rule: f(g(x)) multiplied by g'(x).

Angel (5 years ago)

@NetworkRedeemer - Because he took the derivative of the inside (5x-1)

arsalan ali (5 years ago)

u are the BOSS!!!!!!

Jay Vics (5 years ago)

5 is the derivative of the inside, [5x-1], which needs to be done when you are using the chain rule. dy/dx [5x-1]= 5.

MylesAllSmiles (5 years ago)

why did you multiply by 5?

Grigoiri Zakharov (5 years ago)

I was looking at my book with a blank stare for like 30 mins. THANK YOU, I LOVE YOU

Okay?Whatever (5 years ago)

Wow! Thank you so much! You have no idea how amazing you are to me right now.

Emma Graves (5 years ago)

This video was the best! Thanks so much for sharing!

purplefire5 (5 years ago)

srry didn't explain that well, it wasn't "new" to me i did factoring before (starting in grade 10) but the factoring i did was for simple quadratic equations, and then later on (advanced functions grade 12) the remainder theorem etc. so i know how to factor, but i was confused on how exactly he got the final answer using the factoring like when he was "cleaning" everything up and simplifying, so i wanted more practice on that, and that's why i asked for further videos on this

YEUHNBD (5 years ago)

where do you go to school ? the us ?

purplefire5 (5 years ago)

...what's you're point? I'm taking grade 12 calculus at the moment and the factoring involved in this chapter (this was a while ago) was new to me,i asked about the factoring so that i could have further practice on it

YEUHNBD (5 years ago)

factoring is grade 10 math...this is g12 or university math

YEUHNBD (5 years ago)

simplifying is the biggest bitch

YEUHNBD (5 years ago)

do engineers in real life ever use this math ???

Silas Chime (5 years ago)

Thank you very very much .
I needed this explanation

funkyfunkhouseoffunk (5 years ago)

I love you. So much help!!

maxwell0700 (6 years ago)

where did that five come from up top?

JazzyRoooo (6 years ago)

I just want to thank you so much! Your videos really helped a lot

Darkpain6 (6 years ago)

you deserve PhDs :)

Francis Alvarez (6 years ago)

saw your own site sir the list is perfect i don't have to search from the other site non stop just click there then take some minutes then i get it

purplefire5 (6 years ago)

do you have any videos that further explain and focus on the factoring, i'm alright with algebra but i'm kind of confused with the factoring thnx!

Elizanette Lopez (6 years ago)

What would I do without these videos?!

Mofola1 (6 years ago)

for those who don't mind....i came up with a faster way to get the answer f(x) = x^4(5x-1)^3
basically add the powers 4+3=7, multiply 7*5x =35x, and 4 by second term which is
4*-1= -4, subtract an x from x^4 which is x^4 - x =x^3
and (5x-1)^3-1=2
final answer is= x^3 (35x-4) (5x-1)^2
thumbs up for others to see

Hani (6 years ago)

sorry my bad I owe him :) lol
excuse my english. thanks for correcting me.

N1G3L2 (6 years ago)

wait what? HE owes YOU? how does that work?

I am Pseudo (6 years ago)

Look up derivative of a constant and the power rule. Think of 5x^1 use the power rule on that by itself and you get 1*5 and then subtracted by the derivative of a constant, that was practice paying off mostly.

patrickJMT (6 years ago)

i am pretty sure i have already, just look around

crabbs patts (6 years ago)

Can you have a harder example for this? Thanks :D

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