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).

View More On Wikipedia.org
Recent contents Top users
  1. A

    B Quick question about calculus (derivatives)

    I thought Differentiation is all about understanding it in a graph. Every time I solve a question on differentiation I visualise it as a graph so it's more logical. After all, that IS what the whole topic is about, right? Or am I just wrong? But when you look at these questions...
  2. K

    Differentiation with respect to a complex expression

    Homework Statement Homework Equations $$(x-a)(x+a)=x^2-a^2$$ The Attempt at a Solution I have to express ##~\displaystyle x^2+16=f\left( \frac{x}{x-1} \right)## I guess it has to be ##~\displaystyle \left( \frac{x}{x-1} \right)^n-a~## or ##~\displaystyle \left( \frac{x}{x-1} \pm a...
  3. Oats

    Show that this function is differentiable

    Homework Statement [/B] 2. The attempt at a solution I'm not really sure where to start. We just want to show that ##\lim_{x \to c} \frac{f(x) - f(c)}{x - c} = 0##. I see that ##\lim_{x \to c} (x - c)^2 = 0##. I feel that this may be a simple trick of inequalities, but I am having a complete...
  4. H

    Find the equation of a cubic graph

    Homework Statement ##x^3 - 4x^2 + ax + b## tangent to x-axis at x = 3 Homework EquationsThe Attempt at a Solution if the graph tangent at x = 3, means at x =3, y = 0 my questions is, is at x = 3 the graph's gradient (slope) = 0 ? if yes why? if yes then means dy/dx = 0 ##3x^2 - 8x + a = 0##...
  5. M

    What is Implicit Differentiation for a Circle?

    Homework Statement Hello I have this circle with the equation : [/B] (x-a)^2+(y-b)^2=r^2 I want to find dy/dx for it 2. Homework Equations (x-a)^2+(y-b)^2=r^2 The Attempt at a Solution I am looking on the internet and it appears that I should use what is called "Implicit differentiation"...
  6. R

    Alternate way of differentiating x^y

    Homework Statement : [/B]find the dy/dx of xy=a constantHomework Equations : basic differentiation formulae[/B]The Attempt at a Solution :[/B] I know we can use logarithmic differentiation for differentiating x y..But can we differentiate it using chain rule and get answer as yxy-1.dy/dx =0. ?
  7. DavideGenoa

    I Differentiation under the integral in retarded potentials

    Hello, friends! I know, thanks to @Hawkeye18 who proved this identity to me, that, if ##\phi:V\to\mathbb{R}## is a bounded measurable function defined on the bounded measurable domain ##V\subset\mathbb{R}^3##, then, for any ##k\in\{1,2,3\}##, $$\frac{\partial}{\partial r_k}\int_V...
  8. DavideGenoa

    I Laplacian of retarded potential

    Dear friends, I have found a derivation of the fact that, under the assumptions made in physics on ##\rho## (to which we can give the physical interpretation of charge density) the function defined by $$V(\mathbf{x},t):=\frac{1}{4\pi\varepsilon_0}\int_{\mathbb{R}^3}...
  9. Blockade

    B Is dy/dx of x2+y2 = 50 the same as dy/dx of y = sqrt(50 - x2)?

    For implicit differentiation, is dy/dx of x2+y2 = 50 the same as y2 = 50 - x2 ? From what I can take it, it'd be a no since. For x2+y2 = 50, d/dx (x2+y2) = d/dx (50) --- will eventually be ---> dy/dx = -x/y Where, y2 = 50 - x2 y = sqrt(50 - x2) dy/dx = .5(-x2+50)-.5*(-2x)
  10. P

    MHB Edin's question via email about implicit differentiation

    (a) Differentiate both sides of the equation with respect to x: $\displaystyle \begin{align*} \frac{\mathrm{d}}{\mathrm{d}x} \left[ y^3 + y + x\,y^2 \right] &= \frac{\mathrm{d}}{\mathrm{d}x} \left[ 10 + 4\sin{(x)} \right] \\ 3\,y^2\,\frac{\mathrm{d}y}{\mathrm{d}x} +...
  11. EEristavi

    Basic Calculus: Differentiation usage

    Problem: How fast is the area of a rectangle changing if one side is I0 cm long and is increasing at a rate of 2 cm/s and the other side is 8 cm long and is decreasing at a rate of 3 cm/s?I have 2 approach and I want to know which is correct, why and what am I missing
  12. binbagsss

    Differentiation / Chain rule - Splitting Logarithms

    Homework Statement Use the top line to get 1) and 2) Homework Equations above The Attempt at a Solution So for 2) split the log up using ##log (AB)=log (A) + log (B) ## and this is simple enough I think I may be doing something stupid with 1) though. I have ##\frac{\partial}{\partial...
  13. S

    Velocity, momentum and energy values for a Pendulum swing

    Homework Statement This is my 'carrying out a practical investigation' assignment for Maths. I've attached the coursework (what I've wrote up to now) and my main concern is whether I've got the right differential equation to find 3 new velocity values throughout the pendulum trajectory...
  14. A

    MHB Differentiation of infinite series

    Find derivative of y=✓{x+✓[y+✓(x+...)]}infinite. Here root comes for total inter terms
  15. awholenumber

    B Some doubts about these differentiation steps

    First of all there is an equation Then there is the derivative Then there is a point slope formula to find the equation of the tangent line Point slope formula to obtain the tangent line . y=3a2(x-a)+a3 Then Plug in the x coordinate into the derivative to get the slope f'(1) = 3(1)2 f'(1) = 3...
  16. kupid

    MHB Calculus & Diff. Eqn: Beginner Qs on Function, Derivative & Gradient

    I have some beginner doubts about Calculus and Differential equations . Is a function always a curve ? Doesn't a function already has a slope ? d/dx of a function gives the gradient of the curve between two points ? The derivative ,d/dx ,The gradient , is the rate of change of a...
  17. Z

    I Do normal differentiation rules apply to vectors?

    (I am not very sure if this is a high-school level question or a undergraduate level question. Sorry.) Does our normal differentiation rules, like the product rule and quotient rule apply to vectors? Say for example, differentiate ##r \times \dot r## ##r## is radius vector, ##\dot r## is the...
  18. binbagsss

    Statistical Mech- basically a differentiation /integral q

    Homework Statement See attached. to get ##p## I need to differentiate ##F## w.r.t ##V##, but I also have that the upper limit ##T_{D}## depends on ##V##, so I must take this into consideration when doing the differentiation. The solution looks as though it has done this without evaluating...
  19. S

    I Understanding the Notation in Lagrangian Differentiation

    I'm just in need of some clearing up of how to differentiate the lagrangian with respect to the covariant derivatives when solving the E-L equation: Say we have a lagrangian density field \begin{equation} \mathcal{L}=\frac{1}{2}(\partial_{\mu}\hat{\phi})(\partial^{\mu}\hat{\phi}) \end{equation}...
  20. F

    Algorithmic differentiation in unsteady heat equation

    Homework Statement Okey her we go I was given a base code called heat_equation_primer. The goal is to implement a optimizer into the program. The two methods that are going to be used is the Quasi-Newton and Steepest descent with search line. So I need gradients. So I tried to differentiate as...
  21. M

    A Time differentiation of fluid line integrals

    I am looking at a proof from a book in fluid dynamics on time differentiation of fluid line integrals - Basically I am looking at the second term on the RHS in this equation $$ d/dt \int_L dr.A = \int_L dr. \partial A / \partial t + d/dt \int_L dr.A$$ The author has a field vector A for a...
  22. Debaa

    B Implicit differentiation or just explicit?

    How do I figure whether to do implicit differentiation or just explicit?? Thanks for the answer.
  23. Mr Davis 97

    I Solving a definite integral by differentiation under the integral

    Say we have the following integral: ##\displaystyle \int_0^1 \frac{\log (x+1)}{x^2+1}##. I know how to do this integral with a tangent substitution. However, I saw another method, which was by differentiating ##f## under the integral with respect to the parameter ##t##, where we let...
  24. D

    Differential calculus ,Successive differentiation

    <Moved from a technical forum, therefore no template.> How is it coming (-1)^n(p+n-1)!/(p-1)! please help...!
  25. K

    I Can Taylor series be used to get the roots of a polynomial?

    I'm using this method: First, write the polynomial in this form: $$a_nx^n+a_{n-1}x^{n-1}+...a_2x^2+a_1x=c$$ Let the LHS of this expression be the function ##f(x)##. I'm going to write the Taylor series of ##f^{-1}(x)## around ##x=0## and then put ##x=c## in it to get ##f^{-1}(c)## which will be...
  26. FritoTaco

    Implicit Differentiation: How Do I Solve \dfrac{x^2}{x+y}=y^2+8?

    Homework Statement \dfrac{x^2}{x+y}=y^2+8 Homework Equations Quotient Rule: \dfrac{g(x)\cdot f'(x)-g'(x)\cdot f(x)}{(g(x))^2} Product Rule: f(x)\cdot g'(x)+g(x)\cdot f'(x) The Attempt at a Solution \dfrac{(x+y\cdot\dfrac{dy}{dx})(2x)-(1\cdot\dfrac{dy}{dx})(x^2)}{(x+y\cdot...
  27. Math Henry

    Differentiation question

    Homework Statement [/B] Summarizing: two civilizations hate each other, one of the civilizations throws a curse at the second. The second civilization succumbs to chaos and has a change in Population each week of ΔP= -√P. That is: Pn = Pn-1-√Pn-1 Homework Equations [/B] Considering that the...
  28. Theia

    MHB What is the Differentiation Challenge?

    Let's have a snack challenge for a while. ^^ Let x and y be real numbers (with restrictions y \ne 0, \ y \ne -x) and \frac{x - y}{x + y} = \frac{x + y}{y}. Find \frac{\mathrm{d}y}{\mathrm{d}x} in whatever form you like most. I mean, for example forms \frac{\mathrm{d}y}{\mathrm{d}x} = f(x, y)...
  29. M

    A Deriving Expression for Differentiation and Summation in Special Case

    Dear Friends So, i have this special case where i have to do a differentiation and summation. Please check the following. Is it okay ?? Or, i how should i proceed with this ?
  30. M

    A How do i perform differentiation over summation?

  31. J

    Implicit differentiation of many variables

    Homework Statement For the given function z to demonstrate the equality: [/B]As you see I show the solution provided by the book, but I have some questions on this. I don't understand how the partial derivative of z respect to x or y has been calculated. Do you think this is correct? I...
  32. Siddharth Rajvanshi

    I Ideal Gas Law and Differentiation

    Is it possible to calculate the rate of change of n with respect to rate of change of Pressure and rate of change of Temperature with V unknown but constant by PV = nRT? Rate of change of Pressure and rate of change of temperature can be measured. R and V are constants.
  33. I

    I Implicit differentiation

    Hey, I found a thread about part of what I'm trying to ask long ago: https://www.physicsforums.com/threads/implicit-differentiation.178328/ Basically, I noticed that if you multiply by x or by y in an equation before implicitly deriving, you get two different answers. Unfortunately their whole...
  34. Dopplershift

    Partial Differentiation Laplace Equation Question

    Homework Statement Consider the Laplace Equation of a semi-infinite strip such that 0<x< π and y>0, with the following boundary conditions: \begin{equation} \frac{\partial u}{\partial x} (0, y) = \frac{\partial u}{\partial x} (0,\pi) = 0 \end{equation} \begin{equation} u(x,0) = cos(x)...
  35. E

    A Understanding the Cost Function in Machine Learning: A Practical Guide

    Could someone please help me work through the differentiation in a paper (not homework), I am having trouble finding out how they came up with their cost function. The loss function is L=wE, where E=(G-Gest)^2 and G=F'F The derivative of the loss function wrt F is proportional to F'(G-Gest)...
  36. R

    Implicit Differentiation Question

    Homework Statement I am told to find dy/dx by implicit differentiation where: e^(x^2 * y) = x + y Homework Equations The above equation and the ln of it.The Attempt at a Solution e^(x^2 * y) = x + y (x^2 * y)ln(e) = ln(x+y) x^2 * y = ln(x+y) x^2(dy/dx) + y(2x) = 1/(x+y) * (1 + dy/dx)...
  37. andrewkirk

    Insights Partial Differentiation Without Tears - Comments

    andrewkirk submitted a new PF Insights post Partial Differentiation Without Tears Continue reading the Original PF Insights Post.
  38. S

    Partial derivatives and chain rule

    Homework Statement a. Given u=F(x,y,z) and z=f(x,y) find { f }_{ xx } in terms of the partial derivatives of of F. b. Given { z }^{ 3 }+xyz=8 find { f }_{ x }(0,1)\quad { f }_{ y }(0,1)\quad { f }_{ xx }(0,1) Homework Equations Implicit function theorem, chain rule diagrams, Clairaut's...
  39. U

    MHB Find the derivative using implicit differentiation (with inverse trig functions)

    Here is the question: This is the step I came to after taking the derivatives and doing some simplification: ^ I did the work myself on paper, I just couldn't type out the whole thing clearly so that anyone else can see what I'm referring too... so I used some online tool to show that...
  40. Q

    Second Derivative (Implicit Differentiation)

    Homework Statement Find y'' Homework Equations 9x^2 +y^2 = 9 The Attempt at a Solution y' 18x+2y(y')=0 y'=-18x/2y y'=9x/y For the second derivative, I get the correct answer (same as the book) up until the very last step. Here's where I'm left at: -9( (-9x^2 - y^2) / y^3 ) The book then...
  41. T

    Implicit Differentiation Question

    << Mentor Note -- thread moved from the technical math forums at OP request, so no Homework Help Template is shown >> x2y + xy2 = 6 I know we use the chain rule from here, so wouldn't that be: (d/dx)(x2y + xy2) = (d/dx)(6) so using the chain rule of g'(x)f'(g(x) and the d/dx canceling out on...
  42. B

    I What is the difference between d/dx and d/d(x^2) in differentiation notation?

    Hi members, see attached PdF file. What's the difference between d/dx and d/d(x^2) I don't understand this notation?? Thank You
  43. Clara Chung

    Rate of change problem (differentiation)

    Homework Statement Refer to the photo, please verify my answer Homework Equations calculus The Attempt at a Solution For c, can I do it by assuming Ah=V. A(dh/dt) + h(dA/dt) = dV/dt then find dA/dt?
  44. Q

    Implicit differentiation (beginner)

    Homework Statement Find y' ... X^2+y^2=25I understand (I think) implicit differentiation, but there is one issue which hangs me up. I've done this before and this is just a refresher as my last calculus course was four years ago. From what I understand, 2x+2y(y')=0 But why isn't it...
  45. M

    I What is the Explanation for Implicit Differentiation Equation?

    First of all thanks for the help, i have a problem finding a good explanation of de ecuation (d/dx)f=(∂f/∂x)+(∂f/∂y)*(dy/dx) could anyone write me a good explanation of this ecuation? thanks for the help
  46. D

    I Difficulty with function dependencies f(u,x)

    If you have a function x = x(u,t) then does u necessarily depend on x and t? so u = (x,t) For example, if x(u,t)=u^2 t it seems that because t=x/u^2 , t=t(x,u) I am having difficulty working out the general equation for dz \over dx if z=z(x,y,t) x=x(u,t) y=y(u,v,t) The chain rule...
  47. Romanopoulos Stelios

    Differentiation of unitary operator U(t,t') in Peskin and Schroeder

    How the authors came to the conclusion (eq. 4.25) that $$ U(t,t')=e^{iH_0(t-t_0)} e^{-iH(t-t')} e^{-iH_0(t'-t_0)} $$
  48. J

    Simple Harmonic Motion - Getting Acceleration from Velocity

    Homework Statement I am doing an experiment where I am measuring the force a speaker is exerting when it is driven by a certain voltage and frequency, so my voltage and frequency values are known. I am assuming the speaker is undergoing SHM and I am measuring its peak to peak velocity...
  49. A

    B (ASK) Implicit Differentiation

    What is ##\frac{d}{dx}(\frac{x}{y^2})##? Please tell me is it correct or not: ##\frac{d}{dx}(\frac{x}{y^2}) = \frac{[\frac{d}{dx}(x)] ⋅ (y^2) - (x) ⋅ [\frac{d}{dx} (y^2)]}{(y^2)^2}## ## = \frac{(x) ⋅ (y^2) - (x) ⋅ (\frac{d}{dy} (y^2)) ⋅ \frac{dy}{dx}}{y^4}## ##= \frac{xy^2 -...
  50. D

    I Differentiation is Exact or Approximation

    Is Differentiation exact or just an approximation? I am wonder whether this question is meaningful or not. Slope is expressed as "it is approaching to a value as x is approaching 0" so it is inappropriate to ask such question. But when I deal with uniform circular motion, it is very confusing...
Back
Top