Partial Derivatives and the Gradient of a Function

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  • เผยแพร่เมื่อ 23 ธ.ค. 2024

ความคิดเห็น • 179

  • @KidDroskii
    @KidDroskii 4 ปีที่แล้ว +85

    "The gradient is kind of like a slope for a higher-dimensional function" is just what I needed to hear to conceptualize this. Thanks!

  • @adityaadit2004
    @adityaadit2004 4 ปีที่แล้ว +168

    Best 10 minutes and 56 seconds of my life. Such a clear explanation!

    • @SumriseHD
      @SumriseHD 8 หลายเดือนก่อน +3

      Fuck Intercourse, watching Dave is the real deal ❤

  • @strugglingcollegestudent
    @strugglingcollegestudent 2 ปีที่แล้ว +29

    This man carried me through general chemistry, calculus II and now calculus III. I can't thank you enough for teaching me math.

  • @onesun3023
    @onesun3023 4 ปีที่แล้ว +103

    Gradient: A vector made up of all the partial derivatives of the function. Thank you!

    • @ycombinator765
      @ycombinator765 4 ปีที่แล้ว +3

      Wtf is Jacobian then??

    • @Darkev77
      @Darkev77 4 ปีที่แล้ว

      Pendulum theSimpleOne lmk when you get an answer

    • @tejaswinikarpe3911
      @tejaswinikarpe3911 3 ปีที่แล้ว +7

      @@ycombinator765 jacobian is something that we use while changing the cartesion coordinates to some polar coordinate system or transforming to any other system.. it gives the amount of change that occurs in area after transforming. Eg: if cartesion coordinates are converted to spherical polar coordinates we have to substitute rho^2 sin(phi)d(rho)d(phi)d(theta) for dxdydz.

    • @ankitaaarya
      @ankitaaarya 3 ปีที่แล้ว +1

      @@Darkev77 he got the answerrrrr seeee

    • @Darkev77
      @Darkev77 3 ปีที่แล้ว +1

      @@ankitaaarya beast

  • @davidbowman9695
    @davidbowman9695 4 ปีที่แล้ว +450

    So good this explanation makes MIT lectures look like an overpriced DLC pack

    • @maxcl3474
      @maxcl3474 3 ปีที่แล้ว +3

      🤣

    • @aashsyed1277
      @aashsyed1277 3 ปีที่แล้ว +1

      ho can proffeser dave explains heart this comment?!

    • @samsonlawal1600
      @samsonlawal1600 3 ปีที่แล้ว +16

      Man said "DLC Pack" lmao

    • @saf8514
      @saf8514 3 ปีที่แล้ว +11

      same with Harvard lectures lmao

    • @hemantsharma17
      @hemantsharma17 2 ปีที่แล้ว +5

      totally agree.. he explains algebra so nicely..i tend to sleep when i listen Glibert's lecture :-)

  • @kahdargo7
    @kahdargo7 5 ปีที่แล้ว +40

    This is awesome. Feel like I finally understand the gradient now.

  • @StephenGillie
    @StephenGillie 5 ปีที่แล้ว +57

    Calculus has been independently created/discovered at least 4 times (Pascal has a programming language named after him for his version) and thus we have 4 completely independent, yet internally consistent, sets of notating these concepts. Why did it get reinvented? Lack of local higher mathematics textbooks and education. Thank you for helping to fill this void in the current age, and making a 5th time unnecessary.

    • @Terry_Hastur
      @Terry_Hastur ปีที่แล้ว

      That's cool to know. Thanks.
      Thanks to you too Professor Dave.

  • @GAment_11
    @GAment_11 4 ปีที่แล้ว +3

    I just went down and liked every comment that was positive on this video. Its the only way to extend my appreciation! Thanks man!

  • @idealthinker101
    @idealthinker101 2 ปีที่แล้ว +7

    He taught in such a visual way... !
    I couldn't "understand" this concept in my 6 months course of Partial Differential Equations. So I just crammed some formulas and just passed the exams.

  • @sreedhar75perupally
    @sreedhar75perupally 2 ปีที่แล้ว +6

    Dave Sir 👍🙏
    Sir you are not just a Professor, in fact you are God sent Educator for all the students & Ex Students like me who studied Calculus 30 years ago ( 1991-1992 ) during my intermediate College days (11th Class ).
    From past two months i have been watching & already watched more than 40 Calculus lessons on your TH-cam Channel.
    Sir i Thank you & Salute You.

  • @danielcheong4804
    @danielcheong4804 2 ปีที่แล้ว +2

    this is what you call a video. One of the best teaching videos I've ever watched

  • @radiacia_3511
    @radiacia_3511 ปีที่แล้ว +14

    dude, you are capable of explaining multivariable calculus to a 15 year old so that he can actually solve questions, youre a God (I'm the 15 year old)

    • @ALLAH-u7k
      @ALLAH-u7k 2 หลายเดือนก่อน

      No he is human

    • @madarauchiha12552
      @madarauchiha12552 หลายเดือนก่อน

      No he is chemistry Jesus... who just happens to be teaching maths too.

  • @jackanderson8278
    @jackanderson8278 3 ปีที่แล้ว +3

    I love how clear and concise your explanations are!

  • @alejandroalmarza8447
    @alejandroalmarza8447 2 ปีที่แล้ว

    Profesor You are amazingly clear…like all my colleagues here say your 10:57 seconds video summarized hours of calculus classes.. my admiration to you. Thanks

  • @goutsugoutsu
    @goutsugoutsu 4 ปีที่แล้ว +3

    Oh thank you so much! After 19 years I can finally picture it!!!

  • @buraxta_
    @buraxta_ 2 ปีที่แล้ว

    the coolest and prettiest explaining teacher I've ever seen!

  • @pulpettedilmare9597
    @pulpettedilmare9597 4 ปีที่แล้ว +14

    You rock man! gracias amigo. Im so happy to finally understand it

  • @josephabboud1151
    @josephabboud1151 3 ปีที่แล้ว +2

    Thank you for all your great videos! I'm studying for finals right now and your videos are infinitely better than my professor who lectures online from his bed. You make it so easy to understand in your great verbal and visual explanations, and your videos bring a lot of fun back into learning! I'm into engineering and I love learning through your videos on biology and astronomy and anything really, because learning is fun and awesome. You're a great teacher, thanks for doing such an amazing job :)

  • @tharunraj9974
    @tharunraj9974 5 ปีที่แล้ว +3

    God!!!!!
    You saved me !!!!!
    I have test tomorrow on this topic !!!!

  • @antonbreugel3332
    @antonbreugel3332 5 ปีที่แล้ว +5

    Hallelujah, just saved my calculus...

  • @AskAKill99
    @AskAKill99 6 หลายเดือนก่อน +2

    2 e to the to z (too easy)thanks for this very well explanation!!!!!

  • @qualitytoolbox4872
    @qualitytoolbox4872 4 ปีที่แล้ว +1

    An eye opener video. Neat and tidy.

  • @sureshtanwar3588
    @sureshtanwar3588 5 ปีที่แล้ว +4

    happy teacher's day sir.....

  • @sotiris41664
    @sotiris41664 2 ปีที่แล้ว

    Even a 14 years old student would understand the gradient of a function with this video. I am not kidding I am 14 and I finally (after 5 days of search in internet) understood what gradient is.

  • @Salamanca-joro
    @Salamanca-joro 8 หลายเดือนก่อน +2

    4:10 if we are treating y^2 as a constant then why are we writing y^2?
    For example if we have this x^2(5)
    5 is a constant so the derivative would be 2x since 5 is constant , and same goes for this question 4:10 , maybe it should have been 1 +3x^2 since y is constant? Instead of y^2+3x^2
    I hope you understood my question

    • @AG-sq2dp
      @AG-sq2dp 5 หลายเดือนก่อน +1

      Yeah, if it's supposed to be constant, I thought won't that become zero?! It did bug me for a while but then I understood that the key point is that even though y is treated as a constant when differentiating with respect to x, the y^2 term does not become 0 in the final PDE equation. This is because we are equating the two partial derivatives, not just looking at the derivative with respect to x alone.

    • @powercables
      @powercables 2 หลายเดือนก่อน

      when taking the derivative in parts you treat y as a constant because your deriving with respects only towards x. say you derive 3x then answer is 3 same with y * x dx (dx = with respects to x) = y. So when taking the derivative of y^2 * x dx you get y^2. if it was y^2 * x^2 dx you would use the power rule only for x becuase your treating y as if its numerical so you would get 2 * y^2 * x. I hope this helped! (sorry if it was confusing)

    • @powercables
      @powercables 2 หลายเดือนก่อน

      also you are right, when deriving a constant without x attachted its 0 so in the equation x^2 + 2xy - y^2 deriving with respects to x you would get 2x + 2y - 0 becuase the y^2 is like a number and the derivative of a number without a pronumeral (that you are treating as a pronumeral not a number so not y in this case) is 0.

    • @lourdjonsalen8465
      @lourdjonsalen8465 หลายเดือนก่อน

      Actually, Product Rule is applied for this one.
      If we have x² + y² and differentiate with respect to x, variable y is a dependent term itself, therefore it becomes 0.
      However let's say we have x²y², it's understandable that we have two different variables in one single term.
      Applying the Product Rule, we'll have:
      u = x²
      v = y²
      *Note that we're still differentiating with respect to x
      vu' + uv'
      (y²)(2x) + (x²)(0)
      *v' which is the derivative of y² with respect to x, becomes 0 according to the constant rule itself
      We're left with
      (y²)(2x) + (x²)(0)
      (y²)(2x) + 0
      = 2xy²
      And we can confirm that x²y² is 2xy² when differentiated with respect to x since we are only differentiating x² and treating y² as constant.

    • @lourdjonsalen8465
      @lourdjonsalen8465 หลายเดือนก่อน

      On the example given in the video, the xy² term consists of two variables; x and y. x is being multiplied to y² in other words.
      u = x
      v = y²
      *Differentiating with respect to x
      vu' + uv'
      (y²)(1) + (x)(0)
      (y²) + 0
      = y²
      We can also confirm it by saying that differentiating xy² with respect to x only affects x which becomes 1 and treating y² as a constant by leaving it alone, thus giving 1*y² or simply y².

  • @te-kowski
    @te-kowski 2 ปีที่แล้ว

    Literally the best explanation. Trying to do a project where partial derivatives come up, and I needed a quick refresher.

  • @Kiky_MedPhysicist
    @Kiky_MedPhysicist 4 หลายเดือนก่อน

    Thank you sir for your dedication and for making this free! 🙏

  • @theologyscienceandpropheti6808
    @theologyscienceandpropheti6808 5 ปีที่แล้ว +3

    Thank you....
    happy teacher's day

  • @Deepak-pi9xx
    @Deepak-pi9xx 3 ปีที่แล้ว +2

    Thank you so much. Finally understood the real meaning of partial derivative and gradient. 😇

  • @Naeem2460
    @Naeem2460 2 หลายเดือนก่อน

    As always professor dave comes in clutch just before the exam 😁

  • @pusheletsommatladi4686
    @pusheletsommatladi4686 4 ปีที่แล้ว +5

    Okay the content of this video is super but the Intro always have me like 😂😎

  • @gandalfthegaytwotowerdestr3391
    @gandalfthegaytwotowerdestr3391 4 ปีที่แล้ว +2

    What a Life saver, thanks so much, professor

  • @Borntowin894
    @Borntowin894 4 ปีที่แล้ว +1

    Was the video time 11 mins😲I didn't have a feeling that 11 mins have passed by. it was deeply interesting.thanks sir🤗

  • @LibertarianGearhead
    @LibertarianGearhead 23 วันที่ผ่านมา

    Omg I finally got it, and I got the comprehension correct on the first try!! Can't believe it!!

  • @santinacasari311
    @santinacasari311 ปีที่แล้ว

    Valeu!

  • @ryannkohlman5751
    @ryannkohlman5751 4 ปีที่แล้ว +2

    Wow great explanation. Sucks to see us students pay for an education where profs have a hard time explaining clearly. Thank You!!

  • @sstein5866
    @sstein5866 4 ปีที่แล้ว +8

    Great explanation! Just one question: Why does the gradient point in the direction of maximum slope?

    • @fineartpottamus9020
      @fineartpottamus9020 4 ปีที่แล้ว +8

      due to the addition of the partial derivative vectors using laws of vector addition

    • @carmelwolf129
      @carmelwolf129 3 ปีที่แล้ว

      @@fineartpottamus9020 this was the final puzzle piece for me, now it all clicked together. thank you a lot.

    • @carultch
      @carultch ปีที่แล้ว

      Directional derivatives tell you what the slope will be, along a given direction among the input variables. Taking a sweep across all possible directions, you'll see that the maximum possible directional derivative occurs when the direction among the input variables is parallel to the gradient.
      To find a directional derivative, you form a unit directional vector, and take its dot product with the gradient vector. As an example, consider the function z = x^2/8 + y^2/4, at the point (1, 1). Suppose we're interested in a direction that is along the diagonal of a 3-4-5 triangle, that is roughly 37 degrees from the +x direction. Our unit directional vector (u) would therefore be given by u = . The gradient at this point is . So the dot product gives us 0.4 + 0.24 = 0.624. This is the directional derivative of this particular function.
      The maximum possible directional derivative at this point, will have the same direction as the gradient. Its unit vector will be . Taking the dot product with the gradient, and we get 0.75/sqrt(5) = 0.335. This is the maximum possible rate of ascent.

  • @devanshujoshi8393
    @devanshujoshi8393 3 ปีที่แล้ว +1

    This is highly underrated stufffff
    Ngl I’m lucky i found this 🔥 I subscribed❤️

  • @Dennis4Videos
    @Dennis4Videos 4 ปีที่แล้ว

    Clear as water, helps me understanding Deep Learning!

  • @abdullahalaraz7404
    @abdullahalaraz7404 7 หลายเดือนก่อน +1

    But I don't understand why x axis + y axis vector will point to the direction of maximum change?

  • @Siigrit
    @Siigrit 6 หลายเดือนก่อน +1

    These videos make me rethink my life choices. Uni is actually ass.

  • @elenaroyss7810
    @elenaroyss7810 10 หลายเดือนก่อน

    Thank you very much! It is the best explanation of partial derivatives that I ever heard!

  • @JoshVandever
    @JoshVandever 3 หลายเดือนก่อน

    Del means gradient. Thank you for clearing that up for me.

  • @banderfargoyl
    @banderfargoyl 4 ปีที่แล้ว

    I have to admit that I've never understood why we have partial derivatives but not partial integrals. With the integral, the dx makes it clear which variable we're integrating and we don't need a special integral sign in addition.

  • @con_el_maestro3544
    @con_el_maestro3544 ปีที่แล้ว

    I watch this channel so much that I once had a dream and your theme song made a cameo 😂

  • @amanjmullick2930
    @amanjmullick2930 5 ปีที่แล้ว +10

    Do you teach all subjects?👍good work btw....

  • @MohammadBenSalamah
    @MohammadBenSalamah 4 ปีที่แล้ว +1

    Excellent explanation!

  • @HeathWatts
    @HeathWatts ปีที่แล้ว

    Nice review of gradients! Thanks!

  • @kaneezfatima926
    @kaneezfatima926 4 ปีที่แล้ว +1

    Wow You have explained very good Finally I understand this concept Keep it up.

  • @abhradeepghosh7102
    @abhradeepghosh7102 3 ปีที่แล้ว

    The lecture is awesome. Clear and precise. But the answer to the gradient of the function at (4, 1) should be (1/2, 0) cause ln(1)=0.

  • @elharithhashim4424
    @elharithhashim4424 8 หลายเดือนก่อน

    Very clear explanation thanks

  • @88NA
    @88NA ปีที่แล้ว

    Thank you Professor Dave

  • @elizabethsimakando7299
    @elizabethsimakando7299 3 ปีที่แล้ว +1

    This is very helpful.
    Why don't you do a video on higher order partial derivatives and total differention

  • @andrii.kukuruza
    @andrii.kukuruza 3 หลายเดือนก่อน

    Great explanation, thanks! However, I didn't quite understand what i, j, and k represent in the equations around the 6th min

  • @nancysanskriti2158
    @nancysanskriti2158 4 ปีที่แล้ว

    Just got to see ur videos sr..... U are an super osm educator... Lots of love ❤😘

  • @FD-rt3rv
    @FD-rt3rv 2 ปีที่แล้ว

    Fantastic explanation

  • @aniketjoshi1610
    @aniketjoshi1610 5 ปีที่แล้ว +7

    Thank you sir!
    I wish you to make vedio on Total differentiation.
    Please !
    Please!
    Please!
    Please!!!!!!!!!

    • @coolwinder
      @coolwinder 5 ปีที่แล้ว +3

      Yeah, I get the gradient, but I am not sure I do total differential. You can also mention gradient of an error function of a neural network, as an example.

  • @MinhLe-xk5rm
    @MinhLe-xk5rm 4 ปีที่แล้ว +1

    wow, amazing video. please keep making more ML videos!

  • @simantajenaadvancedmathema9764
    @simantajenaadvancedmathema9764 5 ปีที่แล้ว +1

    Good explanation sir

  • @Jojo_clowning
    @Jojo_clowning 4 ปีที่แล้ว +1

    6:00 you confused me there f(x,y) is a 3 dimension function taking 2 inputs, f(x,y,z) is a 4 dimensions function with 3 inputs.
    How does the grad vector get expressed in the previous 3d graph if we can't calculate the partial derv in z (df/dz) with the k unit vect.

    • @debarpan
      @debarpan 4 ปีที่แล้ว +2

      Mr Booshit He probably meant a function that varies with three different variables (as in dimensions or axes).

    • @xOxAdnanxOx
      @xOxAdnanxOx 4 ปีที่แล้ว +1

      Yes it’s like when you have a component in the z direction that you care about, they are all still 3D I think

    • @CROMast3r
      @CROMast3r 4 ปีที่แล้ว +1

      f(x,y) is a surface in 3D, not the 3D itself

  • @rigbyb
    @rigbyb 7 หลายเดือนก่อน

    Really helpful video, thanks so much :)

  • @sambananas4513
    @sambananas4513 5 ปีที่แล้ว +1

    Thanks for making that so simple for me @ 59. Cheers!

  • @vikramnagarjuna3549
    @vikramnagarjuna3549 5 ปีที่แล้ว +1

    Thanks sir, clarified. Please do on line integrals and Greens theorem..

  • @ZYau-lc5ql
    @ZYau-lc5ql ปีที่แล้ว

    Hello, why does the grad f(x,y) have the component of z-direction? I mean if the gradient of f(x,y) points in the direction of maximum change, that would be a z-direction.

    • @carultch
      @carultch ปีที่แล้ว

      Gradients of a function of multiple variables, are limited to the space of the input variables. The gradient of f(x, y) only exists in the x-y plane. It represents stuff that is happening in the z-direction, when f(x, y) is represented as the z-position in a 3-D spatial coordinate system, but the gradient itself doesn't exist in the z-direction.

  • @mathadventuress
    @mathadventuress 4 ปีที่แล้ว +4

    I'm only in calc 2, and we barely started with differential equations... Interesting

  • @yamatanoorochi3149
    @yamatanoorochi3149 8 หลายเดือนก่อน

    product: u' v + v' u
    division: (u' v - v' u)/v²
    I find it easier to memorize like this
    u prime v plus v prime u has a ring to it

  • @mrhatman675
    @mrhatman675 4 ปีที่แล้ว

    Omg now that I know what it s definition and what it means I can work out what these beatifull weird equations mean thank you!!!!!!!!

  • @omer7895
    @omer7895 2 ปีที่แล้ว

    How would you find the gradient of f(x(s),y) is it still d/dx, d/dy or will the chain rule need to be applied?

  • @GoBlue402
    @GoBlue402 4 ปีที่แล้ว

    what do the i, j , and k represent in the grad f formula? (5:56)

    • @ProfessorDaveExplains
      @ProfessorDaveExplains  4 ปีที่แล้ว

      the unit vectors along the three axes

    • @GoBlue402
      @GoBlue402 4 ปีที่แล้ว

      @@ProfessorDaveExplains So does the length of the vectors stay the same along each gradient. Sorry if I am not understanding something correctly

    • @carultch
      @carultch 3 ปีที่แล้ว

      @@GoBlue402 The vectors i, j, and k, are unit vectors that identify directions in the three cardinal axes of x, y, and z. Some books choose to hat the letters x, y, and z, to avoid a separate letter. It is an artifact of history that we call the unit vectors i-hat, j-hat, and k-hat.
      By definition, a unit vector has a magnitude of 1. This could be the axis unit vectors, or it could also be unit vectors in general. A unit vector's purpose is to identify direction, so it can give direction thru scalar multiplication to what otherwise would be a scalar quantity. Another application of unit vectors is in Newton's law of gravitation, and analogously, Coulomb's law, where r-hat is used as the radial unit vector, because the force acts radially along the line joining the two bodies.

  • @trollthiti8045
    @trollthiti8045 10 หลายเดือนก่อน

    very good explanation i am from india/

  • @shlokekhullar4261
    @shlokekhullar4261 2 ปีที่แล้ว

    Thankyouuu soo much professor….absolutely incredible explanation!!!!!

  • @portgasdace8961
    @portgasdace8961 5 ปีที่แล้ว +2

    Just awesome !!!

  • @aniketjoshi1610
    @aniketjoshi1610 5 ปีที่แล้ว +1

    Why are those videos private, in the playlist??????

  • @aiueo8962
    @aiueo8962 11 หลายเดือนก่อน

    Why this is so easyy???? Thanks..

  • @namelessbecky
    @namelessbecky ปีที่แล้ว

    Thank you.

  • @ahmedelsabagh6990
    @ahmedelsabagh6990 4 ปีที่แล้ว

    Great teacher

  • @thevegg3275
    @thevegg3275 4 ปีที่แล้ว +2

    Can someone help clear my confusion?
    When taking deriv wrt x of f(x,y), sometimes we say y is a constant so replace y with zero.
    Other times we say hold variable y as constant (and instead of replacing y with 0, we write down the y.
    This is so confusing!!! Here is clear example of my question. @t

    • @gunjanramteke909
      @gunjanramteke909 4 ปีที่แล้ว +2

      I also noticed it

    • @gunjanramteke909
      @gunjanramteke909 4 ปีที่แล้ว +2

      Please let me know if you find the solution

    • @alman5718
      @alman5718 4 ปีที่แล้ว +3

      Suppose you have f(x) = x^2 + 2. When you find the derivative you will get f'(x) = 2x. The plus 2 is a constant and doesn't affect the gradient of the curve. Furthermore if you have a function for example f(x) = 4x^2. The constant at the front (in this case 4) will affect the gradient so doesn't cancel like adding a constant. So the derivative will be f'(x) = 4*2x = 8x.
      For partial derivatives of x all you're doing is treating y as a constant. just like the '+ 2' and the '4 * ' in the two examples.
      So let's suppose you have f(x,y) = xy + y. From the first example you take the ' + y' as a constant which it's derivative is zero since this won't affect the gradient. While the constant for 'xy' will stay. Making ∂f/∂x = y + 0 = y. Hope this helps.

    • @thevegg3275
      @thevegg3275 4 ปีที่แล้ว +1

      Thanks so here is how I now see it.
      F(x,y)=x^2 + y.
      F'( x)= d/dx (x^2) +d/dx (y)
      =2x+0
      F(x,y)=pi*x^2*y
      F'(x)=pi*y* d/dx (x^2)
      =pi*y*2x

  • @ImadFG204
    @ImadFG204 หลายเดือนก่อน

    I think answer to second question is ?

  • @giorgosrallis7044
    @giorgosrallis7044 3 ปีที่แล้ว

    Great video

  • @ricardo.mazeto
    @ricardo.mazeto 5 ปีที่แล้ว +4

    Del? Aren't those called Nablas?

  • @saritadalwani7847
    @saritadalwani7847 3 ปีที่แล้ว

    Is advanced math platlist multivariable calculus ??

  • @mahendrapanda4443
    @mahendrapanda4443 5 ปีที่แล้ว +1

    Please make a lec on real life application of matrix; projection of 3d image in eigen space and all that.

  • @Imagon100
    @Imagon100 5 ปีที่แล้ว +4

    3:10 so if I have a curvy D does that make me a partial man?

  • @naders.
    @naders. 3 ปีที่แล้ว

    Thank you! 😊

  • @adityashankar5267
    @adityashankar5267 4 ปีที่แล้ว +2

    Finally, prof got a haircut 😂💇💇‍♂️

  • @asaidinesh5220
    @asaidinesh5220 5 ปีที่แล้ว +1

    Hope u make video on divergence and curl of a function, its goona make my visualisation much clear😁...by the way tq sir for the gradient video...😇

  • @kevconn441
    @kevconn441 5 ปีที่แล้ว +1

    Why do you say sometimes the derivative of the constant is 0, and the derivative of, say x, is x?

    • @ProfessorDaveExplains
      @ProfessorDaveExplains  5 ปีที่แล้ว +1

      the derivative of any constant is zero, and the derivative of x is 1

    • @kevconn441
      @kevconn441 5 ปีที่แล้ว +1

      @@ProfessorDaveExplains Thank you for the reply.
      I think my confusion is whether x is a constant in the original function or being held constant say if you are working out the partial derivative with respect to y.

    • @carultch
      @carultch 3 ปีที่แล้ว

      @@kevconn441 If you are taking the derivative of a function of multiple variables, relative to only one of the variables at a time, you treat all other variables as constants. So when using the d/dy operator, x becomes a constant in that particular differential operation. It is called a partial derivative when you do this, although the same principle still applies to differentiation in general.

  • @kiliankraus
    @kiliankraus 11 หลายเดือนก่อน

    I was geniuely so proud of myself that I could do the comprehension check lol

    • @kiliankraus
      @kiliankraus 11 หลายเดือนก่อน

      thank-you for this video!

  • @jamespatrick9191
    @jamespatrick9191 3 ปีที่แล้ว

    Hi! just a trivial question, what does "In" in "2xIn(y)" stand for?

    • @kashyaptandel5212
      @kashyaptandel5212 ปีที่แล้ว

      natural log, it’s logarithm of y with base e, (or which power would you raise e to , to achieve y)

  • @kaan7120
    @kaan7120 3 ปีที่แล้ว

    thank you so much you are the best

  • @tanelkagan
    @tanelkagan 2 ปีที่แล้ว

    Curious - what does using the "curly d" really add here? Could we not have done exactly the same thing using the standard d/dx, d/dy notation?
    What (I think) I am trying to say is that since we *know* we're dealing with a multivariable function, is it even possible that the standard d/dx (etc) notation could be misunderstood as referring to the "derivative of the whole function" even if that made any sense?
    The gradient sort of does that, so if we're looking at derivatives w.r.t. x and y, what do we gain in the intermediate steps by changing to "curly d"s?
    Or am I overthinking this, and we use curly ds purely as a label to remind ourselves that we're in a multivariable problem? Seems odd, should you need reminding if you're at this level of calculus!? 🤔

  • @clkhaalaqtimir4677
    @clkhaalaqtimir4677 2 ปีที่แล้ว

    thanks professer dava i d,not more engish but iunderstand

  • @scrambledsocks9295
    @scrambledsocks9295 ปีที่แล้ว +6

    where is "he knows a lot about science stuff" :(

  • @coxixx
    @coxixx 4 ปีที่แล้ว

    is it true that gradient always points to summit of function?

    • @carultch
      @carultch 3 ปีที่แล้ว +1

      The gradient points in the path of steepest ascent. This could mean that it points to a peak of a function, and not necessarily the global peak of a function. It could simply point to a local maximum. It could also mean that it points to a saddle point of a function, where the function has two opposite curvatures meeting. It could also point to a local maximum on the function that is a continuous line, rather than a point-maximum.

  • @simonediblasi8198
    @simonediblasi8198 ปีที่แล้ว

    That's a huge amount of knoweledge

  • @coolwinder
    @coolwinder 5 ปีที่แล้ว +1

    This is great, I have exam on 13th, can you make some more videos public :D

  • @sauravprashar
    @sauravprashar 3 ปีที่แล้ว

    I haven’t done derivatives in school yet so I am a bit confused that why is gradient of 2 variable function a 3d curve?

    • @sauravprashar
      @sauravprashar 3 ปีที่แล้ว

      Ok got it we simply plot it in the 3d space like
      Z = f(x, y)

  • @SunitaSaran-t3d
    @SunitaSaran-t3d 2 หลายเดือนก่อน

    4.5

  • @vpa956
    @vpa956 4 ปีที่แล้ว

    Explained it.

  • @MiltosPol-qn3zh
    @MiltosPol-qn3zh 5 ปีที่แล้ว +5

    What are i, j and k ???

    • @ProfessorDaveExplains
      @ProfessorDaveExplains  5 ปีที่แล้ว +2

      ooh that's explained earlier in the series, check out the ones on vectors in my mathematics playlist, a bit before the calculus content starts, or possibly after calculus and before linear algebra

    • @DankFloyd-fe9bi
      @DankFloyd-fe9bi 5 ปีที่แล้ว +3

      Unit vectors. It's a vector with a magnitude of one. These particular unit vectors point in the X, y and z directions and give you another way to notate other vectors. For example, you could write the vector as 2i+5j+4k

    • @MiltosPol-qn3zh
      @MiltosPol-qn3zh 5 ปีที่แล้ว +2

      @Diogenes TheDog I understand almost 90% of calculus(you know what I mean, even some difficult multiple integrals and relatively difficult problems on them) and even the last advanced maths video proffesor dave uploaded but i find vectors really difficult to understand so i have many queries like this one