# 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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38. ### 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. ### 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. ### 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. ### MHB 2.6.5 Implicit differentiation

$\tiny{166.2.6.5}$ 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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)