Differentiation by the Chain Rule

[@rasitylcn2120]

I watch you from Turkey, I like your energy, now I solve the questions with you. :)

[@davidcolf8362]

Great explanation of the chain rule. And I so appreciate your inclusion of biblical verses at the end of each video. God bless you, PN.

[@lano-i4x]

istg u have saved my life sir no teacher nowadays actually cares if students learn math they js teach the lesson dryly and go on about their day thank u so much keep up the good work

[@DigbyWood-v6k]

You can initally take a 5 out of the logarithm, so you get f(x)=5ln(sec(x^4-1)). Thats why the derivative is much simpler, there was an inital simplification.

[@Grecks75]

True, it saves you one application of the chain rule.

[@BartBuzz]

Nicely done. A perfect video for applying the chain rule.

[@wafflaaar1067]

pretty wild stuff... differentiating a composite function like that results in a much simpler looking function

[@jaymincorn4379]

I love doing these questions mentally and then seeing your process Thank you for the video

[@maburwanejohannes4647]

Fun fact: Integrating the derivative obtained would be much easier.

[@dan-florinchereches4892]

I think using properties of logarithm to pull out the power of 5 before differentiating would make less steps

[@talcual2138]

I love your work, and I think calculus is a better choice than bizarre problems. Go for differential equations, double integrals, Gaussian etc etc. It's a joy following you!

[@teacherheng1688]

Nice sir

[@ThePhotonMan110]

Yesss back to calculus my fav branch

[@vasiledumitrescu9555]

Amazing video as always. I have a question, if you know anything about it: do you think that a bachelor degree in math will give me an adequate preparation to pursue a major in theoretical physics later on?

[@chriscalderon1337]

Next time I would take the power of -5 out of the log first. So f(x) becomes -5 log(cos(x^4 - 1)).

[@momchilcvetanov5965]

yeah and also here a minus comes out, i did it with the fact that sec is 1/cos and still a minus came out. where is it lost bc i cant see a problem with his solve(maybe i am blind)

[@actualRocketScientist]

Hey just wanted to say that I love your videos. I do know most of the stuff because one of my degrees is in math but I still enjoy doing math for fun and yes I know that's weird.

[@arkadeusz91]

Nah man... I like doing math for fun too. It's not weird. Right? RIGHT?!😅

[@actualRocketScientist]

@arkadeusz91 it's all right we can be friends and do math together lol. Currently trying to solve the Riemann hypothesis. I seriously doubt I will figure it out but it's fun to think about nonetheless.

[@yoshi7530]

hardest question is to calulate how many hats he has

[@ivanhuertas5307]

a straw man fallacy... These videos are intended for teaching, learning and we should be grateful for that to the teacher for sharing their time and knowledge, if we don't see it that way let's see another type of videos more in line with what we write... Thank you for your teachings Prime Newton

[@yoshi7530]

@@ivanhuertas5307 wut

[@Vanadist]

​@@ivanhuertas5307 Greatest reply ever

[@justabunga1]

You could have use properties of logarithms first and then differentiate the function to make things a lot easier. By using properties of logarithm, the function is the same as y=5ln(sec(x^4-1)). The derivative of that function is, therefore, y'=(5(4x^3)sec(x^4-1)tan(x^4-1))/(sec(x^4-1))=20x^3tan(x^4-1). The result came out to be the same as before without the properties of logarithms.

[@surendrakverma555]

Thanks Sir

[@Noonecc]

I found the easiest question of his channel🤯🤯

[@asparkdeity8717]

u = x^4 - 1 makes it incredibly easy to both integrate back and differentiate using chain rule

[@Orillians]

yes sir!

[@Musterkartoffel]

I've got a quick question : is there a definite answer if 0 is tetrated to 0? I mean people can't agree on 0^0, so that should be even funnier

[@kabeeralishaikh1439]

😂😂ya i agree

[@holyshit922]

Do you want proposition for differentiation Calculate limit at z = 0 d^n/dz^n z/(exp(z) - 1) This limit should give us formula for Bernoulli numbers

[@nothingbutmathproofs7150]

When using logs to take a derivative you never have to use the power rule (nor the quotient or product rule). You should have brought down the 5!

[@srisaishravan5512]

Lets go! thanks for uploading on calc, i was looking forward for these vids

[@Grecks75]

Watching you teach the basics: Maybe it would have been better to first explain briefly what the chain rule is before applying it in an example? For those who are learning.

[@Metaverse-d9f]

just bring the 5 down (basic log property)，and (ln(secx))'=tanx, how can you differentiate it so slow?

[@allaboinadivakar1976]

Hi sir make videos on combinatorics

[@RyanLewis-Johnson-wq6xs]

Differentiate f(x)=Ln(Sec(x^4-1)) f’(x)=20x^3 tan(x^4-1)

[@harshplayz31882]

Ez