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. S

    Two-Step backward differentiation

    Homework Statement By using Taylor expansion, derive the following two-step backward differentiation which has second order accuracy: \frac{3y_{j+1}-4y_j+y_{j-1}}{2h}=f(t_{j+1},y_{j+1}) Homework Equations Taylor expansion ODE y^{\prime}=f(t,y) , y(0)=\alpha The Attempt...
  2. Shindo

    Use of differentiation operators?

    In Calculus, I am studying differentiation at the moment. The two equations is the basic Derivative function: (f(x+h)-f(x))/h and the alternative formula: (f(z)-f(x))/(z-x); and I can see how they both have their own purposes for finding the tangent line and such; but when will differentiation...
  3. Z

    MHB Complex Step Numerical Differentiation

    Well I think this is really cool, numerical differentiation of real analytic functions by stepping out of the reals: Complex Step Differentiation | Cleve's Corner Even funnier is John D'errico's comment (my amusement is mainly due to the idea that a fourth order finite differences scheme with...
  4. MarkFL

    MHB John's Implicit Diff Q&A: Horiz/Vert Tangents at Yahoo! Answers

    John's question at Yahoo! Answers regarding implicit differentiation & horizontal/vertical tangents Here is the question: I have posted a link there to this topic so the OP can see my work.
  5. C

    Confusion in centre of gravity and centre of mass differentiation

    Hi friends, I have Kinetic energy problem during collision. Please Help me in solving this. Thank you all in advance. The problem is as: https://fbcdn-sphotos-c-a.akamaihd.net/hphotos-ak-frc1/q71/s720x720/1380301_1432382870322152_49372184_n.jpg Attempt...
  6. A

    Implicit Differentiation to find dy/dx

    Use implicit differentiation to find dy/dx given x^2y+xy^2=4. I have no idea how to approach this problem. My instructor assigned this as homework but has not gone over it at all in class. We have gone over explicit differentiation and I understand this well. I have read the section but it is...
  7. Q

    Change in x (Differentiation) - Calc III needed?

    Homework Statement http://i.minus.com/jDtSwpCGlrMhP.jpg Homework Equations Solving for dx/dy (change in x with respect to y) I get a solution that isn't one of the answer choices. The Attempt at a Solution 3y^2 = 8x' + x'/x Coordinate: x = 1 (given) y = 2 (solved for in...
  8. L

    What is the Second Derivative of Implicitly Differentiated Function?

    Homework Statement Determine y'' when 5x^2 + 3y^2 = 4. The Attempt at a Solution So I found the first derivative using the power rule and chain rule, 10x + 6yy' = 0 Which I then solved for y', y' = -10x/6y = -5x/3y Next I found the second derivative using quotient rule...
  9. M

    Is my Differentiation Assignment Correct? - Seeking Feedback from Experts

    Hi! I'm new to the forum so first I would like to say 'Hi' to everyone. I would like to ask you to check my assignment. It is already finished (at least I hope it is). Please do not get me wrong. I don't ask anyone to do any work for me. I'm only asking if it's correct. If any part isn't I...
  10. C

    Exterior differentiation and pullback

    Say one one have a projection map ##\pi : M^5 \to M^4## which in adapted coordinates are of the form $$ \pi(x^\mu, x^4) = x^\mu$$ where ##\mu = 0,1,2,3##. Now if one ##M^4## introduce an orthonormal frame ##\left\{ e_\mu, e_4\right\}## where ##e_\mu## are tangential to ##M^4## and ##e_4##...
  11. L

    Differentiation Problem on Lie Groups

    Suppose θ is a differential 1 form defined on a manifold and with values in the Lie algebra of a Lie group,G. On MxG define the 1 form, ad(g)θ ,where θ is extended by letting it be zero on the tangent space to G How do you compute the exterior derivative, dad(g)θ ? BTW: For matrix...
  12. Saitama

    Simple Partial Differentiation problem

    Homework Statement If ##z=x\ln(x+r)-r## where ##r^2=x^2+y^2##, prove that $$\frac{∂^2z}{∂x^2}+\frac{∂^2z}{∂y^2}=\frac{1}{x+y}$$Homework Equations The Attempt at a Solution Since ##r^2=x^2+y^2##, ##∂r/∂x=x/r## and ##∂r/∂y=y/r##. Differentiating z w.r.t x partially...
  13. M

    Is this differentiation correct?

    Hi, Would you be able to tell me if my differentiation in the attached file correct? Note that N, U and D are constants. I am trying to understand how I changes with a change in S. Thanks.
  14. E

    Differentiation spherical coordinates

    Hi ! I'm trying to inverse a mass matrix so I need to do something like this \dfrac{q}{\partial \mathbf{r}} where \cos q = \dfrac{\mathbf{r}\cdot \hat{\mathbf{k}}}{r} However, when \mathbf{r} = \hat{\mathbf{k}} \text{ or } -\hat{\mathbf{k}} I have problems. ¿What can I do...
  15. A

    Differentiation with convolution operators

    Hello, I have really been banging my head the whole day and trying to figure this derivative out. I have a function of the following form: F = W * (I.J(t)) - (W * I).(W*J(t)) where I and J are two images. J depends on some transformation parameters t and W is a gaussian kernel with some fixed...
  16. C

    Change of variable for 2nd partial differentiation and higher.

    Hello, the question I have arises from the 4th Edition of the book "Advanced Engineering Mathematics" written by K.A. Stroud. For those who owns the book, it is the example #2 starting at page 379. More precisely, the example is separated into two parts but the first one is very straight...
  17. V

    Simple Partial Differentiation Question

    Homework Statement I found this solved example in an old textbook. I don't think that the solution provided is correct. I'll be very grateful if someone could verify it. Question: xxyyzz = c What is \frac{∂z}{∂x}? Solution Provided: Taking logarithms on both sides: zlog(z) =...
  18. T

    Differentiation of a two dimensional inverse function

    Hi I have a question regarding differentiation of inverse functions that I am not capable of solving. I want to prove that \frac{\partial}{\partial y} h_y(h^{-1}_{y_0}(z_0))\bigg|_{y=y_0} = - \frac{\partial}{\partial y} h_{y_0}(h^{-1}_{y}(z_0))\bigg|_{y=y_0}, where h_y(x) is...
  19. MarkFL

    MHB Tangent Line & Log Diff EQs: Jawairia's Qs at Yahoo Answers

    Here are the questions: I have posted a link there to this topic so the OP can see my work.
  20. I

    Jacobian Determinant/ mult. variable implicit differentiation

    Homework Statement Let F: x^2 + y^2 - z^2 + 2xy - 1 = 0 and G: x^3 + y^3 - 5y - 4 = 0. Calculate dz/dx. Note: This is NOT the partial derivative ∂z/∂x. I do not need help in taking the derivative of many polynomials. What I need help in is setting up a Jacobian determinant to evaluate this...
  21. P

    Can we use differentiation in Real analysis?

    I'm a beginner to Real Analysis, My problem is, Can we use differentiation when we have to find Suprimum or Infimum for a given set? A = {(x)^(1/x) | x in N} I got Sup(A) = e^(1/e) by using differentiation. is it a correct way to find Sup(A)? or is there any other way to find Sup(A) ...
  22. MarkFL

    MHB Nth order differentiation challenge

    Let: f(x)=x\sin(x) Derive a formula for: f^{(n)}(x) Using this, infer a formula for: \frac{d^n}{dx^n}\left(x\cos(x) \right) edit: I wanted to make sure it is clearly understood that: f^{(n)}(x)\equiv\frac{d^n}{dx^n}\left(f(x) \right)
  23. MarkFL

    MHB Kartik's Diff. of Cont. Fraction Q @ Yahoo Answers

    Here is the question: I have posted a link there to this topic so the OP can see my work.
  24. P

    Differentiation: the prime notation

    Hi, I have been using, for the most part, the prime notation when I want to indicate differentiation. As off recently, I have gained more insight into Leibniz's notation. This triggered the following question: how does the prime notation indicate what we are differentiating with respect to? I...
  25. Petrus

    MHB Function differentiation, show that....

    Hello MHB, Sorry for the bad title as I did not know what to name this but this is a problem from my calculus exam which I have not decide if I shall travel 2h to get my exam and see if I got some less point then I should.. (I just got the facit for the exam and I think that I am between one...
  26. P

    Implicit Differentiation and the Chain Rule

    Hi, I was trying to understand why the chain rule is needed to differentiate expressions implicitly. I began by analyzing the equation used by most websites I visited: e.g. x2+y2 = 10 After a lot of thinking, I got to a reasoning that satisfied me... Here it goes: From my...
  27. S

    MHB Taylor series: Changing point of differentiation

    Continuing from http://www.mathhelpboards.com/f10/taylor-series-x-%3D-1-arctan-x-5056/: The discussion in that thread gave rise to a general question to me: Does not the point of differentiation change when one makes the substitution h = x -a? I like Serena affirmed this "conjecture but...
  28. P

    Simple Integration and Differentiation Problem

    The question is the following: y = (lower limit 0, upper limit e2x)∫ (1/T) Find y'(2) According to the markscheme, the answer is equal to 4e2. I got 2e2. I did the following: I integrated the expression, which yielded: 2√t. I then substituted the upper and lower limits in, which...
  29. A

    Vout(t) using laplace and differentiation

    Homework Statement Homework Equations V(L)=L*di/dt laplace(u(t))=1/s The Attempt at a Solution was just wondering if i did this right. converted to the s domain, then wrote voltage equation around loop, in terms of current I(s): V(s)=R*I(s)+L(\frac{dI(s)}{dt}-iL(0-))...
  30. J

    Verifying Solution for Partial Differentiation of a Function of x-ct

    Homework Statement y(x,t) = f(x-ct) verify this solution satisfies equation ∂y2/∂x2 = 1/c2*∂y2/∂t2 Homework Equations The Attempt at a Solution ∂y/∂x = ∂f/∂x = 1 ∂y2/∂x2 = 0 ∂y/∂t = ∂f/∂t = -c ∂y2/∂t2 = 0 Is this the way to do it?
  31. F

    Finding the Derivative of (2x)^(2x) using the Chain Rule

    Homework Statement \frac{d}{dx}\, (y = (2x)^{(2x)}) Homework Equations Chain Rule: d/dx (g * x) = g'x + x'g The Attempt at a Solution y = (2x)^{(2x)} 1. Take natural log of both sides. ln(y) = ln(2x)·(2x) 2. Differentiate both sides \frac{dy}{dx}\,·\frac{1}{y}\, =...
  32. F

    Covariant differentiation on 2-sphere

    Consider a 2-sphere S2 with coordinates xμ=(θ,\phi) and metric ds2=dθ2+sin2θ d\phi2 and a vector \vec{V} with components Vμ=(0,1). Calculate the following quantities. ∇θ∇\phiVθ ∇\phi∇θVθ
  33. T

    MHB Differentiation and Integration?

    Really struggling on these 2 questions for a Maths assignment, I've got to find dy/dx. Could anyone help me with the working out and answers please? a) y=3sin(4x)-5+5cos(x/3)+4x b) dy/dx=4cos(2x)+6 (given that y(0)=7)
  34. Z

    MHB Differentiation of (x^3)(y^2)=128?

    Differentiation of (y^4)(x^2)=128? Differentiation of (y^4)(x^2)=128, and then given dy/dx = 4 show c = -2d and find the value of c and d. been stuck on this question for a while now, any help would be appreciated thanks!
  35. D

    A question about implicit differentiation

    So, I understand that implicit differentiation involves derivatives in which x values and y values are mixed up. I've done several implicit differentiation problems a couple sections ago for my math homework, but I pretty just memorized patterns and solved it that way. Now that I'm trying to...
  36. F

    How Do You Simplify Derivatives in Basic Differentiation Problems?

    Homework Statement Differentiate the following and display in the simplest form. Part A: y=0.2x^5 - sin4x + cos4x Part B: y=(2x^4 +3)^3 Part C: y=2x^3 sinx Part D: y=\frac{sinx}{x^2} Part E: y=\frac{x^3}{x^2 +1} Homework Equations chain rule product rule quotient ruleThe Attempt at...
  37. L

    Series soln to d.e. - Index of summation after differentiation

    Homework Statement I am confused about what happens to the index of summation when I differentiate a series term by term. Let me show you two examples from my diff eq book (boyce and diprima) which are the primary source of my confusion: Homework Equations From page 268: The function f is...
  38. D

    Newton and Leibniz approach to differentiation

    Newton and Leibniz both had a method of differentiating. Newton had fluxions and Leibniz had something that resembles the modern derivative. Historically, does anyone know how they went about calculating the derivative?
  39. J

    Analyzing Projectile Motion with Varying Angle and Acceleration in 2D

    Homework Statement A moving point has a position function (P) and is given by 2D quantities where the (Y) axis is affected by gravity (9.8m/s/s) and (t) is in seconds. X(t)=4t cos θ and Y(t)= 4t sin (θ)-5t^2 If θ = Pi /3 find the speed in directions after 10 seconds...
  40. MarkFL

    MHB Josh's question at Yahoo Answers regarding implicit differentiation

    Here is the question: Here is a link to the question: Derive Trig Function? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.
  41. P

    Implicit Differentiation Question - Stuck

    Homework Statement Use implicit differentiation to find y' given y/(x-y) = x^2+1.Homework Equations The Attempt at a Solution Hi, I'm doing an online course for Calculus 12, and I have been struggling with Implicit Differentiation. I am hoping someone could maybe help me. Thanks. I'm not...
  42. P

    Implicit Differentiation Question - Stuck

    Hi, I'm doing an online course for Calculus 12 and I have been struggling with Implicit Differentiation, hoping someone could maybe help me. Thanks. I'm not positive I'm doing this right but maybe someone can point me in the right direction, this is what I have so far y/(x-y) = x^2+1...
  43. B

    Deriving the Rate of Change of Angle in a Rocket Launch Using Differentiation

    The question is as follows: A rocket was launched straight up, and its altitude is given by h = 10 t2 m after t seconds. You are on the ground 300 m from the launch site watching the rocket going up. The line of sight from you to the rocket makes an angle θ with the horizontal. By how many...
  44. L

    Vortices - differentiation of the field in abelian Higgs

    In Zee's "Nutshell QFT" (chapter V.7) or Shifman's book "Avanced Topics in QFT" (section 10) when they talk about vortices, they claim: if \phi(r,\theta) goes to \nuexp( i\theta) as r goes to infinity then \partial_{i}\phi becomes \nu(1/r) I do not see how? Is the phase equal to 1/r if r...
  45. F

    Graphing Functions of Differentiation

    Homework Statement Find the intervals of increase or decrease. h(x)=(x+1)^{5}-5x-2 Homework Equations The Attempt at a Solution I found the derivative to be \begin{align*} h'(x) &= 5(x+1)^{4}-5 \\ &= 5[(x+1)^{4}-1] \\ &= (x^{4}+4x^{3}+6x^{2}+4x+1-1) \\ &=...
  46. 5

    How to Correctly Apply Implicit Differentiation?

    Homework Statement For the curve x2+3xy+y2 = 5 show that \frac{dy}{dx} =- \frac{2x+3y}{3x+2y} Homework Equations N.A. The Attempt at a Solution 2x + 3xy + 2y\frac{dy}{dx} = 0 3x + 2y \frac{dy}{dx} = -2x+ 3y ∴ \frac{dy}{dx} =- \frac{2x+3y}{3x+2y} have I done this correctly?
  47. T

    Calculus problem- Implicit differentiation

    Homework Statement e^y = x(y-1) answer must be in implicit form Homework Equations The Attempt at a Solution I literally have no idea how to do this problem. I have the answer, but that's it. The answer is dy/dx(e^y) = x(dy/dx) + y - 1
  48. M

    Derivative using Logarithmic Differentiation

    Homework Statement http://www.flickr.com/photos/50468243@N02/8577233960/ Homework Equations The Attempt at a Solution In the pic, the noticeable difference between my answer and Wolframalpha's is the tan[log(sin x+1) to base 5]. If I do logarithmic differentiation, what I get is...
  49. G

    Implicit differentiation in multiple variables

    So, as the title may have given away, I'm trying to figure out implicit differentiation in the multiple variable context. I thought a good practice would be the law of cosines, aka c^2 = a^2 + b^2 - 2abcosθ. So I'm trying to find ∂θ/∂a, ∂θ/db, ∂θ/dc. I tried solving for θ and then taking...
  50. S

    How Do You Isolate dy/dx in Implicit Differentiation?

    Homework Statement Use implicit differentiation to find an equation of the tangent line to the curve at the given point. x^2+y^2=(2x^2+2y^2-x)^2 @ (0,(1/2)) Homework Equations The Attempt at a Solution So, I don't have a problem differentiating this. Which I get...
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