The Derivative Equals The Square

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  • Опубликовано: 4 дек 2024

Комментарии • 61

  • @fahrenheit2101
    @fahrenheit2101 Месяц назад +29

    Neat and simple. I suppose one simple thing to add would be the intuition behind the Cauchy product, namely that you could, say, put the terms in a multiplication grid, and the Cauchy product simply adds all terms in the grid by going along the diagonals.

  • @terdragontra8900
    @terdragontra8900 Месяц назад +9

    For any solution to f’(x) = f(x)^2, f(x + c) is also a solution, and the set of all solutions is a one parameter family, so the only functions with this property are 1/(c - x)

    • @silver6054
      @silver6054 Месяц назад +3

      Well, also the trivial functions f(x)=0 which isn't of that form

    • @terdragontra8900
      @terdragontra8900 Месяц назад +1

      @@silver6054 Oh oops! Though if you “let c be infinity” and accept my lack of rigor you do get that, and the one parameter family is now topologically a circle, which is pretty cool.

  • @louthurston8088
    @louthurston8088 Месяц назад +1

    First proof nice and immediate. Second an interesting counting procedure.

  • @Dedicate25
    @Dedicate25 Месяц назад +10

    Your explanation makes things easy to grasp.👏

  • @r2d2slair24
    @r2d2slair24 Месяц назад +15

    Only applicable when |x|

    • @Sir_Isaac_Newton_
      @Sir_Isaac_Newton_ Месяц назад +1

      It also works when x = 0.72927499488311371218371090973371

    • @TheInterestingInformer
      @TheInterestingInformer Месяц назад

      @@Sir_Isaac_Newton_also applicable when x = 0.972762946715444173900173976153849912547988155025108

    • @DonutOfNinja
      @DonutOfNinja Месяц назад +6

      ​@@Sir_Isaac_Newton_The absolute value of a number between and not including 0 and 1 is obviously less than 1

    • @briogochill6450
      @briogochill6450 Месяц назад

      Uh, why ?

    • @r2d2slair24
      @r2d2slair24 Месяц назад +1

      @@briogochill6450 Its a rule for binomial expansion of negative and decimal index.
      Otherwise series will always coverge to infinity.

  • @Fysiker
    @Fysiker Месяц назад +2

    I subscribed when I first saw your video on Lorentz transformations, I appreciate the level of detail you put into your explanations and your clarity stands out.

  • @TheFarmanimalfriend
    @TheFarmanimalfriend Месяц назад +1

    Great explanation. World class. Thank you.

  • @alipourzand6499
    @alipourzand6499 Месяц назад +2

    Ok, this time I subscribed to your channel. First time that I understand the Cauchy thing. ☺

  • @experimentingalgorithm1546
    @experimentingalgorithm1546 Месяц назад +2

    Amazing result, I feel delighted to be your early subscriber

  • @chadx8269
    @chadx8269 Месяц назад +3

    That is beautiful.

  • @Jonas-gm4my
    @Jonas-gm4my Месяц назад +1

    I understood it yippiiiieeee. Great explanation

  • @Vadim_Ozheredov
    @Vadim_Ozheredov Месяц назад +1

    2:29 Microphone distortion leads to EX-CUTE 😂

  • @BerndSchnabl
    @BerndSchnabl Месяц назад +4

    all the way I was thinking ... that's not going to work ... that's not going to work ... that's not going to work ... that's not going to work .... and then .... ooohhh it DOES work 😂

    • @fifiwoof1969
      @fifiwoof1969 Месяц назад +3

      Only if abs(x) < 1
      1/(1-x) isn't continuous

  • @Naman_shukla410
    @Naman_shukla410 Месяц назад +7

    Hey bro it's 3:45 am here good morning 😅

  • @BuddyNovinski
    @BuddyNovinski Месяц назад +2

    Wow! I just came across the piano recital on You Tube from four years ago. I was mispronouncing your first name. I can't understand why I seem to have a mental block on infinite series. Maybe it'll come to me one day. I have the time now to learn this stuff. Years ago, I found out why so many of us can't get math, so I could blame my professors, but I think it's a third the student, a third the text, and a third the professor. I'll always remember that in ten minutes how you explained LaPlace transforms that I could understand, 😀without the "piecewise continuous" confusion and the lack of explaining how the integral works I had back in the fall of 1976, which left me confused for nearly a half century.😵‍💫

  • @ConradoPeter-hl5ij
    @ConradoPeter-hl5ij Месяц назад

    Thanks for making this video

  • @hqTheToaster
    @hqTheToaster Месяц назад +1

    Is it possible to construct a function whose half-order derivative is equal to the sum of its second and third prior result? f(x) {'...' }(1/2) = f(x-2)+f(x-3) ?

  • @leonardobarrera2816
    @leonardobarrera2816 Месяц назад

    thanks dude for this video

  • @Chrisuan
    @Chrisuan Месяц назад

    very nice explanation! more like this please :)

  • @aidarosullivan5269
    @aidarosullivan5269 Месяц назад

    Equation of friction?🤔

  • @ronsmythe7764
    @ronsmythe7764 Месяц назад +1

    Very good.
    Isn't d/dx((1-x)^-1) =-(1-x)^-2

    • @MuPrimeMath
      @MuPrimeMath  Месяц назад +1

      No, because the negative signs from the power rule and from the derivative of 1-x cancel out.

  • @mahdiimaninezhad2433
    @mahdiimaninezhad2433 Месяц назад

    It is better to have a look at geometric aspect of this. Suppose a square with length 1+x+x^2+x^3+.... and try to evaluate the area of the square by its induced partitions.

    • @mab9316
      @mab9316 Месяц назад

      Then you have to derivate another square, but how!?

  • @giuseppemalaguti435
    @giuseppemalaguti435 Месяц назад

    d/dx(1/1-x)=1/(1-x)^2...(1/1-x)^2=1/(1-x)°2

  • @anghme28ang11
    @anghme28ang11 Месяц назад

    Why would the coefficient be n+1

  • @Hatifnote
    @Hatifnote Месяц назад

    Seulement pour série infinie
    Sinon
    1+2x+3x² ≠ (1+x+x²)²

  • @Viki13
    @Viki13 Месяц назад

    Cool result

  • @shishirjha7744
    @shishirjha7744 Месяц назад

    x

  • @Metaverse-d9f
    @Metaverse-d9f Месяц назад +6

    you forgot to mention that the absolute value of x must less than 1..

    • @AbhinavKumar-nh8dl
      @AbhinavKumar-nh8dl Месяц назад +1

      Exactly I was also thinking the same thing

    • @RickyMud
      @RickyMud Месяц назад +2

      @@AbhinavKumar-nh8dli was also thinking of saying I was thinking that this is exactly what I was thinking of saying

    • @TarKrypton
      @TarKrypton Месяц назад +2

      Not necessarily, if you treat the series as formal power series, you don’t have to worry about convergence

  • @elektronikvideos-bremen2873
    @elektronikvideos-bremen2873 Месяц назад +1

    0:30 No, I don't agree. E.g. take x=5 than 1/(1-x)=-0.25 but the sum of all powers will diverge towards infinity.
    More worse: take x=0 and you will "prove" infinity=0 👎

    • @MuPrimeMath
      @MuPrimeMath  Месяц назад +2

      The infinite sum equation holds for |x|

    • @AlgoFodder
      @AlgoFodder Месяц назад

      @@MuPrimeMath If you mentioned "-1 < x < 1" at the start of the video it would have saved me scrolling down here to find this comment! Thanks though :)

  • @tomholroyd7519
    @tomholroyd7519 Месяц назад

    dx is a square matrix [[0, 1], [0, 0]]

  • @archangecamilien1879
    @archangecamilien1879 Месяц назад

    If it's true, lol, and I'm guessing it is, otherwise the video wouldn't say it is, lol...write out the partial sums, etc, do the operations on the partial sums, take the limits, then establish they are the same, etc...

  • @akultechz2342
    @akultechz2342 Месяц назад

    -2/x = S(xⁿ)

    • @akultechz2342
      @akultechz2342 Месяц назад

      Use S(G.P.) formula for x < 1 and solve. Since if x > 1 then LHS -> -1
      RHS -> ±infinity
      Hence x < 1

  • @anghme28ang11
    @anghme28ang11 Месяц назад

    Why is the sum equal to 1/1-x? If i sub in x it clearly is not equal

    • @gowipe-grandcross
      @gowipe-grandcross Месяц назад

      It is equal only if -1 < x < 1

    • @super0spore0fan
      @super0spore0fan Месяц назад

      Say you have a finite sum Sn = 1 + q + q² + q³ + ... + q^n
      Then, by distributive property, q*Sn = q + q² + ... q^(n+1)
      If you subtract Sn from q*Sn, you get a telescoping series, which results in q^(n+1) - 1. (Apply commutative property to aggregate each equal term on both series)
      Simply divide each side by q and you get the result of the original finite sum. Sn = (q^(n+1) - 1)/q
      Now, it happens that if |q|

    • @BridgeBum
      @BridgeBum Месяц назад

      Perhaps you have seen how to solve 1+1/2+1/4+1/8+1/16+...
      That sum is the first value (1) over 1 minus the common ratio (1-1/2) or 2. That formula is 1/1-r = 1+r+r^2+r^3+...
      This only converges when -1

  • @jo5i4h
    @jo5i4h Месяц назад

    nice video i like the huh? cat

  • @anestismoutafidis4575
    @anestismoutafidis4575 Месяц назад

    ∫ (Σ ♾️ /n=0 x^n)•dx =(Σ•1/2• ♾️)^2
    (Σ1/2• ♾️ )^2 = [( ♾️ /2)^2+c]
    [ ♾️^2 /4+c]=[♾️ +c]

  • @거미남자_spidy
    @거미남자_spidy Месяц назад

    🇩‌f=f²......

  • @Metaverse-d9f
    @Metaverse-d9f Месяц назад

    you can try to do the derivative of the geometric series formula with respect to x AND n.

  • @saiello2061
    @saiello2061 Месяц назад

    Stoopid cat... 😁

  • @lucasfrykman5889
    @lucasfrykman5889 Месяц назад +3

    Clean shaven fits you better bro. Embrace your youth when you still have it.