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. P

    Differentiation of functional integral (Blundell Quantum field theory)

    I am reading the Lancaster & Blundell, Quantum field theory for gifted amateur, p.225 and stuck at understanding some derivations. We will calculate a generating functional for the free scalar field. The free Lagrangian is given by $$ \mathcal{L}_0 = \frac{1}{2}(\partial _\mu \phi)^2 -...
  2. S

    Distinguish Leaves vs Leaflets: Objective Criteria

    If I'm informed that a structure on a plant is a leaf with a certain number of leaflets, I can usually visualize the plant that way. But if I'm not informed about that fact, I only see leaves. How can I distinguish leaves vs leaflets?
  3. chwala

    Show that the graph is convex for all values of ##x##

    Part (a) no problem...chain rule ##\dfrac{dy}{dx}= (2x+3)⋅ e^{x^2+3} =0## ##x=-1.5## For part b, We need to determine and check if ##\dfrac{d^2y}{dx^2}>0## ... ##\dfrac{d^2y}{dx^2}=e^{x^2+3x} [(2x+3)^2+2)]## Now any value of ## x## will always give us, ##\dfrac{d^2y}{dx^2}>0## The other...
  4. A

    I Find the roots of the quadratic equation by differentiation

    The Solution of the Quadratic Equation By Differentiation Method
  5. fresh_42

    Insights An Overview of Complex Differentiation and Integration

    I want to shed some light on complex analysis without getting all the technical details in the way which are necessary for the precise treatments that can be found in many excellent standard textbooks. Analysis is about differentiation. Hence, complex differentiation will be my starting point...
  6. chwala

    Exploring an Alternative Approach to Implicit Differentiation

    This is a text book example- i noted that we may have a different way of doing it hence my post. Alternative approach (using implicit differentiation); ##\dfrac{x}{y}=t## on substituting on ##y=t^2## we get, ##y^3-x^2=0## ##3y^2\dfrac{dy}{dx}-2x=0## ##\dfrac{dy}{dx}=\dfrac{2x}{3y^2}##...
  7. G

    Find the two points on the curve that share a tangent line

    IMPORTANT: NO CALCULATORS I assumed two points, (a, f(a)) and (b, f(b)) where b is greater than a. Since the tangent line is shared, I did f'(a) = f'(b): 1) 4a^3 - 4a - 1 = 4b^3 - 4b - 1 2) 4a^3 - 4a = 4b^3 - 4b 3) 4(a^3 - a) = 4(b^3 - b) 4) a^3 - a = b^3 - b 5) a^3 - b^3 = a - b 6) (a...
  8. karush

    Determine the order of differentiation for this partial differential eqn

    ok I posted this a few years ago but replies said there was multiplication in it so I think its a mater of format ##\dfrac{\partial u^2}{\partial x\partial y}## is equivalent to ##u_{xy}## textbook
  9. YouAreAwesome

    B Can a log have multiple bases?

    Hi, I tutor maths to High School students. I had a question today that I was unsure of. Can the natural log be to the base 2? The student brought the question to me from their maths exam where the question was: Differentiate ln(base2) x^2 If the natural log is the inverse of e then how does...
  10. chwala

    Solve the problem that involves implicit differentiation

    My take; ##6x^2+6y+6x\dfrac{dy}{dx}-6y\dfrac{dy}{dx}=0## ##\dfrac{dy}{dx}=\dfrac{-6x^2-6y}{6x-6y}## ##\dfrac{dy}{dx}=\dfrac{-x^2-y}{x-y}## Now considering the line ##y=x##, for the curve to be parallel to this line then it means that their gradients are the same at the point##(1,1)##...
  11. chwala

    Solve this problem that involves implicit differentiation

    The question and ms guide is pretty much clear to me. I am attempting to use a non-implicit approach. ##\tan y=x, ⇒y=\tan^{-1} x## We know that ##1+ \tan^2 x= \sec^2 x## ##\dfrac{dx}{dy}=sec^2 y## ##\dfrac{dx}{dy}=1+\tan^2 y## ##\dfrac{dy}{dx}=\dfrac{1}{1+x^2}##...
  12. manareus

    Estimating maximum percentage error using partial differentiation

    Attempt at question No. 1: ΔD = ∂D/∂h * Δh + ∂D/∂v * Δv ∂D/∂h = 3Eh^2/(12(1-v^2)) ∂D/∂v = 2Eh^3/(12(1-v^2)^2) Δh = +- 0,002 Δv = 0,02 h = 0,1 v = 0,3 ΔD = 3Eh^2/(12(1-v^2)) * Δh + 2Eh^3/(12(1-v^2)^2) * Δv Because the problem asked for maximum percentage error then I decided to use the...
  13. rudransh verma

    B Problem with the concept of differentiation

    We define differentiation as the limit of ##\frac{f(x+h)-f(x)}h## as ##h->0##. We find the instantaneous velocity at some time ##t_0## using differentiation and call it change at ##t_0##. We show tangent on the graph of the function at ##t_0##. But after taking h or time interval as zero to find...
  14. A

    Differentiation of Log(cos(X)/x^2)^2

    Im going by the chain rule. I let y=log(t)^2. T=cos^2x/x^2 Dy/DT is 2/t * log(t) Dt/DX is (sin(2x)/X )((sinx+cosx)/X) Can someone verify this is the correct way ? As when I multiply dydt by dtdx I get an equation I don't know how to simplify
  15. D

    I Partial differentiation and explicit functions

    Hi For a function f ( x , t ) = 6x + g( t ) where g( t ) is an arbitrary function of t ; then is it correct to say that f ( x , t ) is not an explicit function of t ? For the above function is it also correct that ∂f/∂t = 0 because f is not an explicit function of t ? Thanks
  16. rudransh verma

    Problem with differentiation

    First I did drho/dr which is equal to 35.4*10^-12/R. Then I integrated drho by which I got rho=35.4*10^-12. And then the last eqn will be q=rhoV. But the answer was wrong. I have a doubt on the formula I am using for E because that formula is for a point charge or a charged shell.
  17. Istiak

    Find that this partial differentiation is equal to 0

    $$\sum_i (\frac{\partial}{\partial q_i}(\frac{\partial T}{\partial q_j}\dot{q}_i)+\frac{\partial}{\partial q_i}(\frac{\partial T}{\partial q_j})\ddot{q}_i)+\frac{\partial}{\partial t}(\frac{\partial T}{\partial \dot{q}_j})$$ They wrote that above equation is equal to...
  18. Istiak

    Differential position vector

    I had an equation. $$T=\frac{1}{2}m[\dot{x}^2+(r\dot{\theta})^2]$$ Then, they wrote that $$\mathrm dr=\hat r \mathrm dr + r \hat \theta \mathrm d \theta + \hat k \mathrm dz$$ I was thinking how they had derived it. The equation is looking like, they had differentiate "something". Is it just an...
  19. maistral

    I Differentiation formula: Is this a typo?

    Red arrows. The notes initially say that the error term is positive. After substitution of A and C which are clearly positive, the term suddenly became negative...? Is this a typo, or is there a theory behind this?
  20. mcastillo356

    I Understanding a quote about implicit differentiation

    Hi PF A personal translation of a quote from Spanish "Calculus", by Robert A. Adams: It's about advice on Lebniz's notation1=(sec2⁡y)dydx means dxdx=(sec2⁡y)dydx, I'm quite sure. Why (sec2⁡y)dydx=(1+tan2⁡y)dydx? But I'm also quite sure that the right notation for (sec2⁡y)dydx=(1+tan2⁡y)dydx...
  21. N

    Tensor Differentiation

    Summary:: help explaining notation with derivatives. Mentor note: Thread moved from technical section, so no homework template is included Sorry. I did not realize there was a dedicated homework problem section. Should I leave this post here? Basically the following (homework) problem. I...
  22. mcastillo356

    Implicit differentiation: why apply the Chain Rule?

    Hi, PF ##y^2=x## is not a function, but it is possible to obtain the slope at any point ##(x,y)## of the equation without previously clearing ##y^2##. It's enough to differentiate respect to ##x## the two members, treat ##y## like a ##x## differentiable function and make use of the Chain Rule...
  23. T

    Numerical Differentiation: Comparing Central & Other Formulas

    Hello there, I have found a different central differentiation formula for a first derivate from what I am used to seeing and I was wondering if they were the same one. I am struggling to find the Numerical Differentiation formulas (forward, backward and central) in scholarly articles and I have...
  24. PainterGuy

    How does gene regulation result in differentiation of different organs?

    I don't know much about biology but the following two questions have always puzzled me. 1: If each human body cell contains the same genes (from 20,000 to 25,000) then how different cells in different parts of body do different things. A liver cell, for example, does not have the same...
  25. R

    Partial Differentiation -- If w=x+y and s=(x^3)+xy+(y^3), find 𝝏w/𝝏s

    𝝏w/𝝏x=1 and then I wasn't sure about 𝝏x/𝝏s, so I tried implicitly differentiating s: 1=(3x^2)(𝝏x/𝝏s)+y(𝝏x/𝝏s)+x(𝝏y/𝝏s)+(3y^2)(𝝏y/𝝏s) And then I shaved my head in frustration.
  26. D

    Critical points and partial differentiation

    zx = 2xy + y2 -3y = 0 and zy = 2xy + x2 - 3x = 0 Subtracting one equation from the other gives y2 - 3y = x2- 3x ⇒ y (y-3) = x (x-3) This leads to the following solutions ( 0 , 0) , (0 ,3) , (3 , 0) but the answer also gives ( 1, 1) as a solution. What have i done wrong to not get this...
  27. R

    I Complex differentiation

    Let z = [a b]^T be in the 2-dimensional vector space over real numbers, and T a linear transformation on the vector space. Consider $$\lim_{z'\rightarrow \mathbf{0}} \frac{T(z+z')-T(z)}{z'}$$ I argue this could be an alternative definition for complex derivative. To illustrate this, z as a...
  28. jaychay

    MHB Hard problem on partial differentiation

    Can you please help me ? I have tried to do it many times but I end up getting the wrong answer. Thank you in advance.
  29. greg_rack

    B How to learn differentiation and integration in 14 days?

    The detailed list of the concepts I should master I'm attending the last year of high school and I'm currently studying limits. For university test reasons I'll need to study on my own topics such as differentiation and integration... and I have just 14 days to do so! Firstly, do you think it's...
  30. Baums Mizushala

    Point on a graph nearest to the origin

    The Attempt at a Solution I know the answer is supposed to be ##(-1,0)##. However when I differentiate the above expression I get. $$ 2x+{\frac 5 2} $$ Then the shortest distance would be when the expression equates to 0. $$ 2x+{\frac 5 2}=0 $$ I should be getting ##x=-1## but solving for ##x##...
  31. N

    B Confusion on Implicit Differentiation

    I am confused about implicit differenciation in a few ways. The main confusion is why, in the equation ## x^2 + y^2 = 1 ##, when we are taking the derivative of the left side, ## 2x + 2yy\prime ##, are we adding a ## y\prime ## to the 2y but we aren't adding an ## x\prime ## to the 2x? I also...
  32. L

    MHB Differentiation help (stationary points)

    I’m struggling with questions c, e and f. I don’t think I understand how to find stationary points.
  33. L

    MHB Differentiation Help: Find 2nd Derivative

    I can't seem to find the second derivative
  34. M

    I Understanding Gluon Self-Interaction and Quark/Gluon Jet Differentiation

    Hello! Based on QCD we can have gluon self-interaction i.e. a vertex with 3 or 4 gluons. What were the experimental evidences by which the existence of these vertices was confirmed? Also, how does one differentiate between a quark and a gluon induced jet? Thank you!
  35. AN630078

    Finding the gradient to the curve using differentiation

    I have attached a photograph of my workings. I do not know if I have arrived at the right solution, nor whether this is the gradient of f(x) at point P. I think I seem to overcomplicate these problems when thinking about them which makes me lose confidence in my answers. Thank you to anyone who...
  36. Blurry__face14

    Implicit Differentiation

    The working I've tried is in the attachment.
  37. Leonardo Machado

    I Chebyshev Differentiation Matrix

    Hi everyone. I am studying Chebyshev Polynomials to solve some differential equations. I found in the literature that if you have a function being expanded in Chebyshev polynomials such as $$ u(x)=\sum_n a_n T_n(x), $$ then you can also expand its derivatives as $$ \frac{d^q u}{dx^q}=\sum_n...
  38. A

    I The Ratio of Total Derivatives

    If we have two functions C(y(t), r(t)) and I(y(t), r(t)) can we write $$\frac{\frac{dC}{dt}}{\frac{dI}{dt}}=\frac{dC}{dI}$$?
  39. A

    I Questions about Partial Differentiation Operations

    1) If we have two functions C(y, r) and I(y, r) can we write: ∂C/∂I×∂I/∂r=∂C/∂r ? Can we also write ∂I/∂C=1/(∂C/∂I) ?
  40. R

    B Spectral Lines: Scrambling & Differentiation

    How are different elements spectral lines naturally 'scrambled' and then differentiated by observation, into each and every element contained in a 'single' light beam emanating from a light source? Is the term 'single' correct in this context and if not can you explain why?
  41. karush

    MHB 2.6.5 Implicit differentiation

    $\tiny{}$ Find y' $$x^2-4xy+y^2=4$$ dy/dx $$2x-4(y+xy')+2yy'=2x-4y-4xy'+2yy'=0$$ factor $$y'(-4x+2y)=-2x+4y=$$ isolate $$y'=\dfrac{-2x+4y}{-4x+2y} =\dfrac{-x+2y}{-2x+y}$$ typo maybe not sure if sure if factoring out 4 helped
  42. T

    A Exploring the Conditions for Evaluating Commutators with Fermionic Operators

    I found a theorem that states that if A and B are 2 endomorphism that satisfies $$[A,[A,B]]=[B,[A,B]]=0$$ then $$[A,F(B)]=[A,B]F'(B)=[A,B]\frac{\partial F(B)}{\partial B}$$. Now I'm trying to apply this result using the creation and annihilation fermionics operators $$B=C_k^+$$ and $$A=C_k$$...
  43. A

    Implicit Differentiation

    Summary:: van der waals I have a pretty good understanding of implicit differentiation. However I'm stuck on a homework problem and could use some help. [P + (an^2)/V^2][V - nb] = nRT a,n,b,R are constants My professor wants me to take the implicit differentiation of P wrt...
  44. WMDhamnekar

    MHB Differentiation under integral sign

    Hello, How to find formulas for these$\displaystyle\int x^n\sin(x)\, dx, \displaystyle\int x^n\cos(x)\, dx,$ indefinite integrals when $n=1,2,3,4$ using differentiation under the integral sign starting with the formulas $$\displaystyle\int \cos(tx)\,dx = \frac{\sin(tx)}{t}...
  45. Math Amateur

    MHB Differentiating Complex Square Root Function: Bruce P. Palka, Ex. 1.5, Ch. III

    I am reading Bruce P. Palka's book: An Introduction to Complex Function Theory ... I am focused on Chapter III: Analytic Functions, Section 1.2 Differentiation Rules ... I need help with an aspect of Example 1.5, Section 1.2, Chapter III ... Example 1.5, Section 1.2, Chapter III, reads as...
  46. V

    Implict differentiation and price

    For this one I did implicit differentiation. Where I then obtained y'=(-2x-4p)/(4x+3p2). Once I had this I plugged in my values where p is $4 per bag and x is 20 cents. I plugged in my values y'= (-2(20)-4(4))/(4(20)+3(4)2) =-7/16. However when I checked this answer it was incorrect and I am...
  47. EchoRush

    I Questions about implicit differentiation?

    I am new to calculus. I am doing well in my class. I just have a few questions about implicit differentiation. First, why do we call it "implicit" differentiation? Also, when we do it, why when we differentiate a term with a "y" in it, why do we have to multiply it by a dY/dX? What does that...
  48. S

    Determine the range of a function using parameter differentiation

    The strategy here would probably be to find a differential equation that ##f## satisfies, but differentiating with respect to ##x## using Leibniz rule yields ##f'=\int_x^{2x} (-te^{-t^2x}) \ dt + \frac{2e^{-4x^3}-e^{-x^3}}{x}## Continuing to differentiate will yield the integral term again...
  49. jisbon

    Implicit differentiation

    Homework Statement: Let ##\frac{1}{a}=\frac{1}{b}+\frac{1}{c}## If ##\frac{db}{dt}=0.2## ,## \frac{dc}{dt}=0.3## , Find ##\frac{da}{dt}## when a=80 , b=100 Homework Equations: - Since we are supposed to find ##\frac{da}{dt}##, I can deduce that: ## \frac{da}{dt}...
  50. R

    MHB Implicit differentiation question

    Help! Keep running this and getting different answers, and none are right. 2xy^8 + 7xy = 27 at the point (3,1)