Calculus - Finding higher derivatives

[@johnnydough4048]

so you're telling me, it's that fucking easy?! Why doesn't my teacher teach like you! :'(

[@nevm5776]

quick question and need answer asap!! On the video at 9:14 you have only a single number which is 8 and you wrote it down for the final answer,,,, While i have 5 of doubles digits on the one im trying to solve... should I add those 5 together?

[@pritychattaraj9648]

Your Mathematics is brilliant . Thank you for help!

[@abovethesky6142]

That helped me a lot!! Thank you

[@justabunga1]

The notation is wrong when writing 4th derivative or higher. f^4(x) means (f(x))^4. This is a function raised to the fourth power. f^(4)(x) means you are taking the fourth derivative of a function. Note how the parentheses is used around the number in the superscript.

[@MySecretMathTutor]

I find most people are not picky on putting parenthesis around the power as long as its understood these are higher derivatives. A similar thing happens when using the inverse notation for a function.

[@justabunga1]

MySecretMathTutor yep exactly. I also forgot to mention for others for the use of parentheses. The parentheses around the negative number means you are doing anti-differentiation or integrating (whether it's an indefinite or definite integral) n times. If it’s without the parentheses, it means you are taking the reciprocal first and then raise this to whatever power it was given i.e. 1/(f(x))^n except for the -1 exponent (e.g. inverse sine of x to mean arcsin(x) and inverse hyperbolic sine of x to mean arsinh(x)).

[@markovolk9800]

what do you use higer derivatives for!!

[@johnmichaeltwist5086]

Marko Volk Engineering, Physics, Mathematics.

[@johnnydough4048]

ABSOLUTELY NOTHING (Unless you're becoming a scientist, engineer, mathematician, or just trying to pass the subject like me)

[@dominiceustacelacuna914]

Thanks!!

[@PaulMpanza-ti5jl]

Can someone explain me that 5v to the power came from

[@sandhyaranidas1005]

Thank you sir

[@citlali12345]

Thank you!

[@shariqshaikh5715]

Is high derivative and High order derivative are same?

[@MySecretMathTutor]

Yes. We will sometimes say "second order" derivative or simply a "second" derivative by they are the same. :^D

[@dhatridongre8849]

What if you expand the first derivative and then take its derivative, will you get the same answer?

[@BEFreda]

Yes, you will. I did it that way (after pausing the video) then restarted it and saw that he did it differently. So I crossed out my answer and did it his way...but then when I went back to my first answer, it was the same.

[@UltraMaan21]

thank you so much

[@anastasiaanautodidact9856]

Can I ask something really necessary? How does all of those derivatives operate on graphs? My brain is antagonized trying to understand how a derivative can be derived from itself graphically 😅💔 Isn't a derivative basically another way of saying "the tiny difference in the 2 outputs w.r.t the two inputs" till they *almost* are one point? How do I take the derivative of literally one point graphically? I have trouble understanding that Or is it that we get a whole new function with a different slope graphically so we can derive sth from that new function? But still how?

[@MySecretMathTutor]

This video might help out a little bit: kzbin.info/www/bejne/f3zbhJuYp8iInrM Basically you can look at the instantaneous rate of change at each point, and plot it on a new graph. This is the graph of the derivative. :^D

[@anastasiaanautodidact9856]

@@MySecretMathTutor I'll be sure to check it out👌🏻

[@aneeshsrinivas892]

what were they thinking with the higher order derivitive notation f^(n)(x).parentheses do not make enough of a difference(eg:if say f^(2x+1)(x) do i mean d^2x+1/dx^2x+1(f(x)) or (f[x])^2x+1). and what is wrong with saying something like f^4′ (x) for 4th derivitive.

[@justabunga1]

Aneesh Srinivas the parentheses around the number on the superscript means you are taking the nth derivative of a function. If it’s without a parentheses, that means you are taking the function raised to whatever power it is except for the -1 exponent. The -1 exponent is the inverse function just like inverse trig. And inverse hyperbolic trig (or using the prefix arc and ar respectively).

[@samud7041]

Guys how do l get a pattern or formula l can use to obtain the nth term,,surely it will be time consuming to find the 25th derivative using the tutor's method....please help

[@justabunga1]

That depends on what function you are talking about. e.g, the 25th derivative of sin(x) is cos(x). For the 25th derivative of 2^x, it will be 2^x(ln(2))^25.

[@chrislloyd123]

thanks

[@kamaljitkaur4834]

you should also provide proof of formulea using mathematical induction

[@mbusomabuza7273]

best

[@erikw113]

Why does every video start off with cosin or e fuck

[@MySecretMathTutor]

These tend to be some of the "nice" derivatives to look at if you are taking multiple derivatives. If you have something more complicated, then the tough job comes to keeping track of all of the pieces. :^D

[@iandava5186]

Only simple examples 🙁

[@ebrimadem5287]

Ian Dava Exatcly

[@reynaldoespino9613]

galing