Calculus - The chain rule for derivatives
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- čas přidán 21. 09. 2013
- The chain rule can be a tricky rule in calculus, but if you can identify your outside and inside function you'll be on your way to doing derivatives like a pro! Remember to put the inside function into the derivative of the outside function, then multiply by the derivative of the inside.
![The Chain Rule for Derivatives in Calculus - [1-5]](/img/n.gif)
Showed up 10 mins late to class and the professor kicked me out, I think I got more out of these 7 mins than 2 hours in calc. Thanks bro
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@@benp2320 no it's not. This isn't highschool.
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You're the only person who makes calculus videos that explains them competently and makes them simple to follow.
just watched all your derivative videos and i feel much better taking my calc exam next week. great videos and thanks!
how did you do on the exam lol
Weeks of class summed up in an 8 minute video. I appreciate you so much. Feeling considerably less stressed for my exam tomorrow!
how'd your exam go?
@@Haza-rp1cb she failed that shit
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Thanks for making these videos, I have an instructor at my community college that makes videos much like yours for his Hybrid classes, and you do an excellent job explaining and going step by step. Especially sense this whole derivative section is rather hard to grasp. I'll defiantly be going to your website for more help!
Quickest and best way to learn math !! Thanks a ton.
Thank you so much! This actually makes derivatives seem approachable and something that I can actually do.
My calculus professor makes things way tooo complicated and difficult to understand. Your videos help me so much! So clear, instead of his lectures I just listen to your videos :)
For anyone confused at 4:30. when x^ -n the answer is 1 over x^ n .
Yeah because of exponent rules. To get a neg exponent to turn positive, you can divide by it. Like x^(-2) is the same as 1/(x^2). We only do this so we have positive exponents in our final answer. (For anyone confused)
@@ewinter9021 but you also want to rationalize any denominator, so is it standard to show 1/√x or √x^-1?
@@VeritasEtAequitas you could just multiply the term by root x over root x, which gives you x over root x
*root x over x
This was a really good explanation and the way you showed it. I've seen quite a few examples of the Chain Rule being demonstrated on YT but this one is very good.
Thank You for using actual numbers and not sin, cos, and tangent for these.
This makes more sense thank you!!
Thankyou so much sir. It really help me out. Thanks alot. May god bless you with happiness and sucess.
I am a junior in college and this video just SAVED ME. The color coding is EXTREMELY helpful. I feel confident in the chain rule now thank you so much!!!!
Fantastic! I was hoping the colors would help others see the inside and outside of functions. I'm glad I could help out. :^D
Amazing tutorial! Thank you so much
Thanks you improve our reasoning
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This makes sense now. Thank you
Thanks to your excellent explaining.
Thank you so much sir..i was trying to understand this for six month you teach it to me in 1 min....
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Thank you for being very clear and better than my professor.
You dont need a professor to teach this. Average grade 10 students can master this.
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SecretMathTutor. You rock. Simply. Super awesome.
Calculus is one of my favorite branch in mathematics, I'm in 8th class and we didn't study calculus yet, I feel bored in our lesson because I'm so advance now, I enjoy mathematics by solving any hard equations, I like to torture myself through solving really hard equations especially in exponential functions,trigonometry and calculus.
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why do we consider the e as outside function, if I read this (e)^(x^2+1) then I would consider the e as an inside function and the power as an outside, just like in the first example of this video. please explain!
Thank you!
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Excelente colega
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Thank you
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I hear ya. Sometimes you just want the information so you can get going. Keep up the good work. :^D
I hope you all the best and I hope you good health . what is the derivative of y with respect to x for y= (x3+2x2+x)^3 ?
I suggest these steps to find dy by dx
1. bring down the power in the front of the bracket as a multiplier.
or bring down the power to the front of the bracket as a multiplier. it is better to put the preposition (in) or (to) in the above sentence .
2. reduce the power by one
3. multiply the derivative of the inside function.
dy/dx = 3 (x3+2x2+x)^2 (3x2+4x+1)
Would you please recommend and advise me what are the best method to find dy by dx ?
All the best
Moamen Saeed Talha
For the second example, I don’t understand how you got that answer using the 1/2 and -1/2 power.
I would think 5x-3/2 because of * 1/2.
@mattmun12 He multiplied the 5 by the 1/2, but since the (5x-3) had a -1/2 exponent, the square root of 5x-3 went on the bottom and was multiplied by the 2 on the bottom. The 5 went on the top.
but 5 times 1/2 is equal to 2.5. Where did the 0.5 go?
Actually, he forgot to include the -1/2, which would turn into a positive 1/2 when he attaches it to the end of the denominator. Correct answer: 5/2(5x-3)^1/2
Who are you, who are so wise in the ways of science ?
I don't understand the last one. He says the outside function is e^x but it's not. If y=x^2-1. then the outside function is e^y and not e^x and the inside function is x^2-1. Where am I going wrong? what is the broken down g part and what is the f part of f(gx) of this particular example ?
How about this (x^2 + 1)^3 (2x - 4)^4 ??
what is the derivative of the inside? how do you get the last number, i dont understand it. please help
thanks a tonne mate
No problem! Keep up the good work. :^D
Are you from which country ? And iam from 🇮🇳 India ,thank 🙏💕 you sir for this amazing video
love from india
Did you forget the negative sign on the second problem with the - 1/2?
confused about whether an exponent is the outside or inside...the first example you use it as the outside and the third example its the inside
At 6:47 Sorry, but why should we keep the x²-1 on the "e"？
That stays there because its actually the "inside" part of the function for e^(). Think of an exponential function like e^(inside).
love you
Where the hell did that 5 on top come from at 4:33?
+mattmun12 it was multiplied by 1/2 i guess
First apply the -¹/² power to it's inside to get ½ • 1/√(5x-3) • 5. Then multiply the ½ to get = 1/ ( 2 ✓(). Then multiply by 5 and you get 5 / ()
you said the power was the inside for the last example, but the one before that you said the sqrt was the outside, and isn't the sqrt just ^1/2?
+Matt R so wouldn't the sqrt be a power. which before you aid was the inside. but for that example you called it the outside
10/10
5:50
super
Does anyone know how the exponent of 1/2 translates into the square root? Still unsure of this. Thanks!
All exponents that are fractions can be turned into roots. The top is the power and the bottom is the index.
x^(2/3) would be the cubed root of x^2
@@MySecretMathTutor Thank you!
At 3:12 what happened to the 2x??? Aren't u supposed to multiply it by 6x(x^2+1)^2 by 2x???
+MySecretMathTutor you are the best man thanks for this videos and the previous ones for the product and quotient rules
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5 time 1/2 is 2.5 not 2....
Can you point out where you saw this in the video? I checked it over and it appears I just left it as 5/2 in the example. You are correct though. 5 times 1/2 is 2.5. :^D
improve your writing plz, your square and cube almost look the same!!!!
You're a stupid person.Appreciate what you have!