What is Differentiation: Definition and 1000 Discussions

The cluster of differentiation (also known as cluster of designation or classification determinant and often abbreviated as CD) is a protocol used for the identification and investigation of cell surface molecules providing targets for immunophenotyping of cells. In terms of physiology, CD molecules can act in numerous ways, often acting as receptors or ligands important to the cell. A signal cascade is usually initiated, altering the behavior of the cell (see cell signaling). Some CD proteins do not play a role in cell signaling, but have other functions, such as cell adhesion. CD for humans is numbered up to 371 (as of 21 April 2016).

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  1. Kisok

    I Covariant Derivative: 2nd Diff - My Question

    My question is shown in Summary section. Please see the attached file.
  2. A

    A Calculation of Fourier Transform Derivative d/dw (F{x(t)})=d/dw(X(w))

    Calculation of Fourier Transform Derivative d/dw (F{x(t)})=d/dw(X(w)) Hello to my Math Fellows, Problem: I am looking for a way to calculate w-derivative of Fourier transform,d/dw (F{x(t)}), in terms of regular Fourier transform,X(w)=F{x(t)}. Definition Based Solution (not good enough): from...
  3. m4r35n357

    Python Automatic vs Symbolic differentiation

    I thought I would give you guys some justification for why I keep pestering you with this odd numerical technique. I've mentioned its advantages over finite differences quite a few times, so now I am putting it up against symbolic differentiation. Here is a plot of the function ##x^2 /...
  4. Physics lover

    Derivative of a Series: How to Solve for x^n/((x-a1)(x-a2)...(x-an)) in Calculus

    I first solved the first two terms and then i solved the resulting term with the third term and so on.At last i was left with x^n/((x-a1)(x-a2)...(x-an)) .Thrn i took log on both sides and then differentiated both sides with respect to x.I got 1/y dy/dx=n/x -1/(x-a1)-1/(x-a2)...-1/(x-an).But now...
  5. m4r35n357

    Python Doing Automatic Differentiation

    This is a brief interactive session using my ODE Playground, which is my repository of Automatic Differentiation code. It illustrates two solutions of ##\sqrt {2}## with the user-specified function provided via a lambda, using Newton's method and then bisection. Note that the user needs to...
  6. Saracen Rue

    Simple Implicit Differentiation Problem

    Okay so I'm really not sure where I went wrong here; here's how I worked through it: $$\ln\left(y+x\right)=x$$ $$\frac{\frac{dy}{dx}+1}{y+x}=1$$ $$\frac{dy}{dx}+1=y+x$$ If ##\ln\left(y+x\right)=x## then ##y+x=e^x## and ##y=e^x-x## $$\frac{dy}{dx}=y+x-1$$ $$\frac{dy}{dx}=e^x-x+x-1$$...
  7. A

    A Is a C^1 diffeomorphism with f of class C^k also a C^k diffeomorphism?

    I am studying Choquet-Bruhat's Introduction to General Relativity, Black Holes and Cosmology, and I don't follow the hint in Exercise I.2.1: Exercise I.2.1 Let U,V be open subsets of R^d. Prove that a C^1 diffeomorphism f:U-->V with f of class C^k is a C^k diffeomorphism. Hint: ##\partial (f...
  8. J

    Trivial question on differentiating logarithms

    My Question : Shouldn't differentiating ##-log B## give ##\frac{-\delta B}{B}##? (Note : A, B and Z are variables not constants) By extension for ##Z=A^a \,B^b\, C^c## where ##c## is negative, should ##\frac{\Delta Z}Z=|a|\frac{\Delta A}A+|b|\frac{\Delta B}B-|c|\frac{\Delta C}C##?
  9. L

    I Calculus problem differentiation.

    <Moderator's note: Member has been warned to show some effort before an answer can be given.> Hello all. This is my first post in this forum, I am asking for your understanding. I have a problem with the calculus task and I stuck in a dead endso I managed to find a solution on the internet. I...
  10. Math Amateur

    MHB McInerney Example 3.1.5: Multivariable Differentiation Q&A

    I am reading Andrew McInerney's book: First Steps in Differential Geometry: Riemannian, Contact, Symplectic ... and I am focused on Chapter 3: Advanced Calculus ... and in particular on Section 3.1: The Derivative and Linear Approximation ... In Section 3.1 McInerney defines what is meant by...
  11. Math Amateur

    I Multivariable Differentiation .... another example .... McInerney Example 3.1.5 .... ....

    I am reading Andrew McInerney's book: First Steps in Differential Geometry: Riemannian, Contact, Symplectic ... and I am focused on Chapter 3: Advanced Calculus ... and in particular on Section 3.1: The Derivative and Linear Approximation ... In Section 3.1 McInerney defines what is meant...
  12. Math Amateur

    I Multivariable Differentiation .... McInerney Definition 3.1.1 ....

    I am reading Andrew McInerney's book: First Steps in Differential Geometry: Riemannian, Contact, Symplectic ... and I am focused on Chapter 3: Advanced Calculus ... and in particular on Section 3.1: The Derivative and Linear Approximation ... I am trying to fully understand Definition 3.1.1 and...
  13. Math Amateur

    MHB Multivariable Differentiation .... McInerney Definition 3.1.1

    I am reading Andrew McInerney's book: First Steps in Diofferential Geometry: Riemannian, Contact, Symplectic ... and I am focused on Chapter 3: Advanced Calculus ... and in particular on Section 3.1: The Derivative and Linear Approximation ... I am trying to fully understand Definition 3.1.1...
  14. CricK0es

    Derivative of a term within a sum

    Homework Statement [/B] From the Rodrigues’ formulae, I want to derive nature of the spherical Bessel and Neumann functions at small values of p. Homework Equations [/B] I'm going to post an image of the Bessel function where we're using a Taylor expansion, which I'm happy with and is as far...
  15. m4r35n357

    Python More cool automatic differentiation (Hamiltonian)

    Well I think it is cool anyhow ;) Here is a dependency-free variable-order double pendulum simulation in about 120 lines of Python. Have you seen the equations of motion for this system? As usual, this is based on code that I have provided here, but trimmed for maximum impact. Can you see...
  16. Delta2

    I Differentiation and Integration cannot always be swapped

    Well here is my (I hope successful this time ) attempt at 10. e) We consider the function ##f(x,y)=\begin{cases}\dfrac{e^{-x|y|}}{y}, y\neq 0 \\ 0, y=0\end{cases}##. For this function for ##y\neq 0## it is for any ##x##, ##\frac{\partial f}{\partial x}=-\frac{|y|}{y}e^{-x|y|}##. Also it...
  17. Runei

    I Total Derivative of a Constrained System

    Hi all, I was working on a problem using Euler-Lagrange equations, and I started wondering about the total and partial derivatives. After some fiddling around in equations, I feel like I have confused myself a bit. I'm not a mathematician by training, so there must exist some terminology which...
  18. opus

    Differentiation with units- Related Rates problem

    Homework Statement A spherical balloon is being filled with air at a constant rate of ##2cm^3/sec##. How fast is the radius increasing when the radius is 3 cm? Homework EquationsThe Attempt at a Solution This is a problem given and spelled out in my text. However, it seems to be assuming that...
  19. I

    Thermodynamics Pathria Eq.4.5.9

    I'm confused about the mathematics that led to the equation 4.5.9. Specifically, I'm confused about what the variables that describe U are. From the equation I think temperature T(through beta), chemical potential (through alpha), V (through E_s) and N (through... restriction on the...
  20. opus

    Logarithmic Differentiation Problem

    Homework Statement Find the derivative of ##f(x)=\frac{e^x-e^{-x}}{e^x+e^{-x}}## 2. Homework Equations The Attempt at a Solution Please see attached image. The given solution has a 4 in the numerator, and I don't see how I can come across that with the way that I'm going. I think I'm making...
  21. opus

    Find eqn of Tangent Line to graph- Implicit Differentiation

    Homework Statement Find the equation of the tangent line to the graph of the given equation at the indicated point. ##xy^2+sin(πy)-2x^2=10## at point ##(2,-3)## Homework EquationsThe Attempt at a Solution Please see attached image so you can see my thought process. I think it would make more...
  22. sams

    I Vector Diff. Q: Dot & Cross Prod. Differentiation?

    I have a question regarding the dot product and the cross product differentiation. I was wondering whether: $$\frac{d(\vec{A}.\vec{B})}{du} = \vec{A}. \frac{d\vec{B}}{du} + \frac{d\vec{A}}{du} .\vec{B}$$ is the same as $$\frac{d(\vec{A}.\vec{B})}{du} = \frac{d\vec{A}}{du} .\vec{B} + \vec{A}...
  23. navneet9431

    Problem in calculating work done?

    Homework Statement See question number 3 Homework Equations Work Done="integral" F*ds The Attempt at a Solution I tried to solve this question using integration, I have replaced F with "1" and ds with "t^2+2t". So I am stuck in at that step. Please help me differentiate it further or solve...
  24. air79

    Using differentiation to find a general expression

    For this task i have to use differentiation to find a general expression for the rocket's velocity as a function of time. Q. A toy rocket has been launched straight upward. Altitude y as a function of time is given as y=bt−ct2, w b = 81 m/s , c = 4.9 m/s2 , t is time in seconds, y is in meters...
  25. navneet9431

    Problem in applying the Chain Rule

    Homework Statement I am facing problem in applying the chain rule. The question which I am trying to solve is, " Find the second derivative of " Homework Equations The Attempt at a Solution So, differentiated it the first time, [BY CHAIN RULE] And now to find the second derivative I...
  26. sams

    A Partial Differentiation in Lagrange's Equations

    In Section 7.6 - Equivalence of Lagrange's and Newton's Equations in the Classical Dynamics of Particles and Systems book by Thornton and Marion, pages 255 and 256, introduces the following transformation from the xi-coordinates to the generalized coordinates qj in Equation (7.99): My...
  27. IonizingJai

    Implicit differentiation problem

    Homework Statement If ##x\sqrt{1+y} + y\sqrt{1+x } = 0##, then prove that ##\frac {dy} {dx} = \frac {-1}{(x-1)^2}##. 2.Relevant Equations: $$ \frac {dy} {dx} = - \frac {\left (\frac {\partial f}{\partial x} \right)} {\left( \frac {\partial f} {\partial y} \right)}.$$ 3...
  28. R

    I Smoothing Numerical Differentiation Noise

    I am using the "knife-edge" technique to find the intensity profile of a rectangular laser beam. The data that is obtained using this method is power, the integral of intensity. Therefore, to get the intensity profile we must differentiate the data. So, as expected, my data looks like a ramp...
  29. I

    B Can you deduce ##\tan(\theta) = \frac {df} {dx}## from this graph?

    Could someone explain to me how from this graph you can deduce that ##\tan(\theta) = \frac {df} {dx}##. Thanks
  30. N

    On differentiation and indices in field theory

    I'm self-studying field theory and trying to solidify my understanding of index manipulations. So I've been told that there is a general rule: " If the index is lowered on the 'denominator' then it's a raised index". My question is whether this is just a rule or something that can make sense...
  31. shintashi

    B When do we use which notation for Delta and Differentiation?

    I was taking notes recently for delta y/ delta x and noticed there's more than one way to skin a cat... or is there? I saw the leibniz dy/dx, the triangle of change i was taught to use for "difference" Δy/Δx, and the mirror six ∂f/∂x which is some sort of partial differential or something...
  32. L

    MHB Application of Differentiation Problem - Need help

    Hi, I have a problem of which I do not know where to start or how to go about solving it. - The graph of the function equation y=f(x) is shown, where f(x) is a cubic polynomial. The graph cuts through the origin, touches the x-axis at (3,0) and passes through (4,4). a) - Prove that f(x) =...
  33. Voq

    I Why do we use ∂ in partial differentiation for multiple variables?

    Why we write differently d in partial derivation differentiation? Is it because of several variables? Edited by mentor -- the action of finding a derivative is called differentiation.
  34. Math Amateur

    MHB Differentiation on R^n ....need/ use of norms ....

    I am reading Hugo D. Junghenn's book: "A Course in Real Analysis" ... I am currently focused on Chapter 9: "Differentiation on Rn" I need some help with an aspect of Theorem 9.1.10 ... Theorem 9.1.10 reads as follows: The proof of Theorem 9.1.10 relies on the definition of the derivative of...
  35. Math Amateur

    I Differentiation on R^n ....need/ use of norms ....

    I am reading Hugo D. Junghenn's book: "A Course in Real Analysis" ... I am currently focused on Chapter 9: "Differentiation on Rn" role="presentation">Rn" I need some help with an aspect of Theorem 9.1.10 ... Theorem 9.1.10 reads as follows: The proof of Theorem 9.1.10 relies on the...
  36. Math Amateur

    I Multivariable Differentiation - Component Functions ....

    I am reading "Multidimensional Real Analysis I: Differentiation" by J. J. Duistermaat and J. A. C. Kolk ... I am focused on Chapter 2: Differentiation ... ... I need help with the proof of Proposition 2.2.9 ... ... Duistermaat and Kolk's Proposition 2.2.9 read as follows: In the above text...
  37. Y

    MHB Differentiation with square roots

    Hello all, I was trying to find derivatives of two functions containing square roots. I got answers which I believe should be correct, however, the answers in the book differ significantly. The first answer of mine was checked in MAPLE and found correct. My guess that the author made some...
  38. J

    MHB Differentiation / Integration Help

    The curve has a gradient function dy/dx = 2 +q/(5x^2) where q is a constant, and a turning point at (0.5, -4). Find the value of q. option 1 : 2.5 option 2: -2.5 option 3: 0 Option 4: -3 I couldn't find the answer and will need assistance to how the answer can be obtained. I have...
  39. I

    Term for differentiation within the cell

    I understand that the terms "differentiation" and "epigenetic" apply to cells in multicellular environment, and that different DNA is expressed to create distinct features in different cells. What about the process of the creation of distinct features within the cell itself, such as all the...
  40. F

    Point on the curve closest to (18,1)

    Question: Question: Find the point on the curve y=x^2 +1 that is closest to the point (18,1). Please see the image and that’s where I’m stucked- after taking the first derivate. Please solve it further step by step completely. It’d mean a lot.
  41. J

    B Product rule OR Partial differentiation

    I have a very basic knowledge of calculus of one variable . In the chapter on heat and thermodynamics , ideal gas law PV =nRT is given . Then the book says, differentiating you get PdV +VdP = nRdT . The book doesn't explain the differentiation step . I think , there are two ways to...
  42. Hawksteinman

    I Differentiation of sin function where's my mistake?

    I was thinking and came up with this. I know it's wrong but can't find the mistake :( dy/dx sin(x) = cos(x) dy/dx sin(kx) = kcos(kx) So dy/dx sin(3x) = 3cos(3x) Now let Y = 3x dy/dx sin(Y) = cos(Y) = cos(3x) 3cos(3x) = cos(3x) 3 = 1 Where is the mistake?
  43. Peter Alexander

    Critical Points of a Parameter Dependent Integral

    1. The problem statement, all variables, and given/known data Find and categorize extremes of the following function: $$F(y)=\int_{y}^{y^{2}}\frac{1}{\ln^{2}x}dx$$ for ##y>1##. Homework Equations $$\frac{d}{dx}\int_{a}^{b}f(x,y)dy=\int_{a}^{b}\frac{\partial}{\partial x}\left(f(x,y)\right)dy$$...
  44. K

    I Need a help in solving an equation (probably differentiation

    I am trying to find out the interference condition between tool and a part. The below attached snapshot is the equation between interference and machine feed. At dy/dx = 0, I will have max. interference, which I intend to find. Except x and y every alphanumeric character in the following...
  45. peadar2211

    Determine the stability of a fixed point of oscillations

    Homework Statement I have a system of coupled differential equations representing chemical reactions and given certain initial conditions for the equations I can observe oscillation behaviour when I solved the equations numerically using Euler's Method. However, then it asks to investigate the...
  46. S

    I Help please with biocalculus question involving differentiation

    Hi, I was just wondering how one would arrive at the answers to these questions. I have the solution for parts a and b, but not for part c. Suppose that antibiotics are injected into a patient to treat a sinus infection. The antibiotics circulate in the blood, slowly diffusing into the sinus...
  47. Math Amateur

    MHB Differentiation of Vector Valued Functions and Affine Maps - Browder, Definition 8.9 ....

    I am reading Andrew Browder's book: "Mathematical Analysis: An Introduction" ... ... I am currently reading Chapter 8: Differentiable Maps and am specifically focused on Section 8.2 Differentials ... I need help in fully understanding Browder's comments on Definition 8.9 ... ... Definition...
  48. Math Amateur

    MHB Differentiation of Vector Valued Functions - Browder, Proposition 8.12 ....

    I am reading Andrew Browder's book: "Mathematical Analysis: An Introduction" ... ... I am currently reading Chapter 8: Differentiable Maps and am specifically focused on Section 8.2 Differentials ... I need help in proving Proposition 8.12 ... ... Proposition 8.12 and the definitions...
  49. H

    MHB Implicit Differentiation to find equation of a tangent line

    I need urgent help. I have this question: Use implicit differentiation to find an equation of the tangent line to the curve at the given point. \begin{equation} {x}^{2/3}+{y}^{2/3}=4 \\ \left(-3\sqrt{3}, 1\right)\end{equation} (astroid) x^{\frac{2}{3}}+y^{\frac{2}{3}}=4 My answer is...
  50. A

    Finding the approximate change in the perimeter of a circle

    Homework Statement The radius of a circle increases from 3 to 3.01 cm. Find the approximate change in its perimeter. Here's a link to the actual question, in case you need the answer for 6(a) to solve 6(b) http://imgur.com/a/nQt6M Homework Equations Perimeter of circle = 2πr Area of circle =...
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