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. H

    I Is there a mistake in the second equation of (5.139)?

    I believe there is a mistake in the second equation of (5.139). The equation is obtained from (5.138) using the Euler-Lagrange equation ##\frac{d}{dt}\frac{\partial L}{\partial\dot{\theta}}=\frac{\partial L}{\partial\theta}.## LHS##\,\,=\frac{d}{dt}\frac{\partial...
  2. C

    Implicit partial differentiation

    Homework Statement in the notes , 'by applying chain rule to LHS of the above equation ' , which equation is the author referring to ? it's given that f /x + (f/z)(z/x) = 0 , As we can see , the function contain variable x , y and z Homework EquationsThe Attempt at a Solution why not f /x +...
  3. redtree

    A Help with covariant differentiation

    I'm having trouble evaluating the following expression (LATEX): ##\nabla_{i}\nabla_{j}T^{k}= \nabla_{i} \frac{\delta T^{k}}{\delta z^{j}} + \Gamma^{k}_{i m} \frac{\delta T^{m}}{\delta z^{i}} + \Gamma^{k}_{i m} \Gamma^{m}_{i l} T^{l}## What are the next steps to complete the covariant...
  4. P

    I Why do we differentiate in physics and why twice?

    I have a basic understanding of the reason why we look for derivative or integration in Physics, based on the water flow example, where integration is the process of accumulating the varying water flow rate "2x" , while we reverse to the water flow rate by differentiating " x squared " the...
  5. E

    I How to Convert this Derivative?

    I have a derivative of a function with respect to ##\log \left(r\right)##: \begin{equation*} \frac{dN\left(r\right)}{d \log\left(r\right)} = \frac{N}{\sqrt{2\pi} \log\left(\sigma\right)} \exp\left\{-\frac{\left[\log \left(r\right) - \log\left(r_M\right)\right]^2}{2...
  6. S

    Find expression in terms of time for a particle's velocity?

    Homework Statement A particle moves along a straight line so that its acceleration t seconds after passing a fixed point O on the line is (2 - 2t) cm/s2. Three seconds after passing O, the particle has a velocity of 5 cm/s. Find and expression, in terms of t, for the velocity of the particle...
  7. M

    MHB Differentiation equation: equation of motion

    a particle of mass m is projected towards a point O with initial speed √5/3 m/s from a point P where [OP]=3 metres. the particle is repelled from O by a force of magnitude 4m/x³ where x is its distance from O. (i) show that the equation of motion is v dv=4x^-3 dx (ii) find how close the particle...
  8. M

    MHB How Do You Calculate the Speed of a Car Based on the Differentiation Equation?

    a car starts from rest. when it is at a distance s from its starting point its speed is v and its acceleration is 25v+v³. show that dv=(25+v²)ds and find (correct to 2 decimal places) its speed when s=.01 this is how i went about it dv/dt= acceleration dv/dt=dv/ds×ds/dt=v×dv/ds v dv/ds=25v+v³...
  9. Udhaya

    Alkalis and bases differentiation

    Hi, I have a doubt on the topic of bases and alkalis. I have learned that a alkali is a soluble base so does that mean Sodium Oxide(Solid) is a alkali and Lithium Hydroxide(Solid) is a alkali. Or are they considered alkali when they are dissolved? For example, Sodium Oxide becomes sodium...
  10. 9

    Differentiate trigonometric equation

    Homework Statement a) Differentiate the following equation with respect to: 1) θ 2) Φ 3) ψ (Ua - Ub)' * C * r where: C is a 3 x 3 rotation matrix: [ cos θ cos ψ, -cos Φ sin ψ + sin Φ sin θ cos ψ, sin Φ sin ψ + cos Φ sin θ cos ψ] [ cos θ sin ψ, cos Φ cos ψ + sin Φ sin θ sin...
  11. L

    B Simple question about differentiation of trigonometric function

    Explain to me: Why the 2πf came in front? I lost touch and sort of forgot.
  12. Parsifal1

    Urgent help please -- Differentiation technique question

    I'm revising differentiation for tomorrow, I am hopelessly stuck on some things. I have some examples with answers, but I have no idea which rules are being used. y=2sin3x dy/dx=6cos3x I see that sin goes to cos but why is the two multiplied by the 3 (if that's what's happening)...
  13. P

    B Does Methane Gravitationally Differentiate in Air or Mix with Fluid Dynamics?

    Does methane gravitationally differentiate in air, or does fluid dynamics mess things up & make it mix in with the air?
  14. S

    Differentiation application problem

    Homework Statement An inverted cone has a depth of 10cm and a base radius of 5cm. Water is poured into it at the rate of 1.5 cm^3/ min. Find the rate at which level of water in the cone is rising, when the depth of water is 4cm. Homework EquationsThe Attempt at a Solution [/B] I know that...
  15. S

    MHB Differentiation with fractions, radicands, and the power chain rule

    Differentiate the following two problems. 1. x divided by the square root of x squared+ 1 2. The square root of x + 2 divided by the square root of x - 1 Thank you.
  16. M

    B A simple differentiation and partial differentiation

    Hi, in the above why is the left-hand side simple differentiation, i.e V is only function of t but in the right it is function of t, x, y, and z. It is very strange that one side is different than the other. Would you like to explain it? Thank you.
  17. P

    MHB Kamal's Questions via email about Implicit Differentiation

    Since we have this relationship between x and y, as the two sides are equal, so are their derivatives. We just have to remember that as y is a function of x, any function of y is also a function of x, with the inner function "y" composed inside whatever is being told to do to the y. So to...
  18. S

    A Differentiation of a product of 4-gradients wrt a 4-gradient

    I know that ##\frac{\partial}{\partial (\partial_{\mu}\phi)} \big( \partial_{\mu} \phi\ \partial^{\mu} \phi \big) = \partial_{\mu} \phi##. Now, I need to prove this to myself. So, here goes nothing. ##\frac{\partial}{\partial (\partial_{\mu}\phi)} \big( \partial_{\mu} \phi\ \partial^{\mu}...
  19. Bounceback

    Differentiation under the integral sign problem

    Homework Statement \int_1^2 \frac {e^x}{x}\,dx Through the use of differentiation under the integral sign. 2. The attempt at a solution Tried inputting a several times, each one resulting in another function without an elementary anti-derivative (example given below) I(a)=\int_1^2 \frac...
  20. P

    MHB Effie's question via email about Implicit Differentiation

    To perform implicit differentiation we must make use of the chain rule. Basically if you have a function composed in another function, its derivative is the product of the inner function's derivative and the outer function's derivative. All other rules (such as the sum rule, the product rule...
  21. NatFex

    I Related Rates (+Trig) Question

    I'm a bit iffy with the whole of the 'related rates' topic of my calculus course. I've tried coming up with a question of my own to see if I can solve it. The question is as follows: The distance between a point on the ground and the bottom of a pole is 26m. The angle of inclination from that...
  22. D

    Differentiation and integration

    Homework Statement Hi,I saw a statement in my physics notes like this(Anyway it is a maths problem): where L is a general differential operator.G is a green's function(I guess it is irrelevant) My question is related to the red line: Suppose we have this: ∂/∂x ∫ f(x-y)g(y) ∂y is it...
  23. DavideGenoa

    MHB A double differentiation under the integral sign

    Hello, friends! Let $k:\mathcal{O}\times\mathbb{R}^n\to\mathbb{R}$, with $\mathcal{O}\subset\mathbb{R}^m$ open, be such that $\forall x\in\mathcal{O}\quad k(x,\cdot)\in L^1(\mathbb{R}^n) $, i.e. the function $y\mapsto k(x,y)$ is Lebesgue summable on $\mathbb{R}^n$, according to the usual...
  24. StanEvans

    I Magnitude of the Second Derivative

    So to find the x values of the stationary points on the curve: f(x)=x3+3x2 you make f '(x)=0 so: 3x2+6x=0 x=0 or x=-2 Then to find which of these points are maximum or minimum you do f ''(0) and f ''(-2) so: 6(0)+6=6 6(-2)+6=-6 so the maximum has an x value of -2 and the minimum has an x value...
  25. R

    MATLAB How Accurate is Numerical Differentiation of sin(x) at 0.4?

    I am trying to estimate the second derivative of ##sin(x)## at ##0.4## for ##h=10^{-k}, \ \ k=1, 2, ..., 20## using: $$\frac{f(x+h)-2f(x)+f(x-h)}{h^2}, \ \ (1)$$ I know the exact value has to be ##f''(0.4)=-sin(0.4)= -0.389418342308651.## I also want to plot the error as a function ##h## in...
  26. DavideGenoa

    I Differentiating twice under the integral (with assumptions)

    Let ##k:\mathcal{O}\times\mathbb{R}^n\to\mathbb{R}##, with ##\mathcal{O}\subset\mathbb{R}^m## open, be such that ##\forall x\in\mathcal{O}\quad k(x,\cdot)\in L^1(\mathbb{R}^n) ##, i.e. the function ##y\mapsto k(x,y)## is Lebesgue summable on ##\mathbb{R}^n##, according to the usual...
  27. I

    Did tissues arise from other cells or cell differentiation?

    Hi I have a pretty specific question. It is in regards to tissues in multicellular organisms. Is there any information on how different cell grouping arose in multicellular organisms? I have some ideas from what I've so far read and learned: - Would this have happened because two different...
  28. N

    Digging deeper into (implicit) differentiation and integration

    Hello all, Here's something I've been trying to wrap my head around: In general, it seems that integration is 'harder' than differentiation. At least analytically. Numerically it may be the other way round. For one thing, it's often easy to differentiate implicit functions. For example...
  29. Z

    Euler-Lagrange question about strange differentiation

    I'm watching Susskind's Classical Mech. YouTube lecture series and am really confused about something he's doing where otherwise I've followed everything up until this point without a problem. In Lecture 3 he's dealing with the Euler-Lagrange equation applied to minimizing the distance between...
  30. L

    Differentiation of exponential

    Plz give me an easy explanation I do know about the differentiation and second differentiation. I just don't get how that negetive sign comes in front of the exponent in the second differentiation
  31. R

    MHB What is the process to solve \sqrt{x}+\sqrt{y}=5 for the point (4,9)?

    Hello! Can someone help me with the process of solving \sqrt{x}+\sqrt{y}=5 on point (4,9)? With implicit, I differntiated both sides and ended up with 1/2x^-1/2+1/2y^-1/2\d{y}{x}=0 and I tried to isolate the dy/dx, but how do I get rid of the others? And with explicit, I isolated y to one side...
  32. I

    Basic implicit differentiation question

    So it has been quite a few years since I learned about implicit differentiation so the content is a bit rusty in my mind. x=rcos(θ) How do you find dx/dt? I know the answer but I am trying to figure out why. I mean dx/dt can be written as (dx/dθ)*(dθ/dt) so why is the answer not just...
  33. M

    Surface area of a spherical cap by integration

    hi guys, i have a question. i saw this picture, and i don't really understand how they derived with the formula. The aim is basically to find the formula for the surface area of a spherical cap. why do you differentiate the x=sqrt(rˆ2-yˆ2)? how does that help to find the surface? and then...
  34. R

    MHB Help on Related Rates implicit differentiation

    Hi! I recently came upon this problem : the height of a right angled triangle is increasing at a rate of 5cm/min while the area is constant. How fast must the base be decreasing at the moment when the height is 5 times the base? I drew a picture of the triangle, labelled the height (h) and...
  35. G

    MHB How do I differentiate $\cos(x+y)$?

    If $y^2+\cos(x+y) = 1$ find $\frac{dy}{dx}$. How do I differentiate $\cos(x+y)$ bit?
  36. X

    Implicit Differentiation z=f(x/y) meaning

    Mod note: Moved from the Homework section 1. Homework Statement This might seem like a stupid question but I'm unsure what z= ƒ(x/y) means? I'm not sure how I would find ∂z/∂x , ∂z/∂y just from this statement either. Thank you Homework EquationsThe Attempt at a Solution
  37. I

    Simple differentiation mistake?

    The working out states that v = (m/r)sin(theta) but surely this should be (-m/r)sin(theta) ? I mean there is a negative in front of the ∂Ψ/dx ? Also, if v=0 then 0 = (m/r)sin(theta), therefore sin(theta) = 0? And from this we know cos(theta) = 1 or -1 which would mean u = Uinfinity + (m/r) or...
  38. Nemo1

    MHB Application of Differentiation - Points of Inflection.

    Hi Community, I have this question. When I graph it I get: When I answer the first sets of questions a, Intercepts: x=(-6), x=0, x=6 Stationary points: (0,0) , (-3\sqrt{2}, -324) , (3\sqrt{2}, -324) Points of inflection: x=0 This is where I was wrong. (It's a turning point isn't...
  39. iwantcalculus

    Implicit differentiation question with inverse trig

    Homework Statement Homework Equations The Attempt at a Solution Note: by real solution I mean the correct implicit derivative, not an actual real solution... Please help![/B]
  40. chwala

    Differentiation and integration of implicit functions

    1. Given the function ##xy+cos y+6xy^2=0## , it follows that ## dy/dx=-y/x-siny+12xy##2. My problem is how do we integrate this derivative ## dy/dx=-y/x-siny+12xy## to get back the original function3.## ∫dy/dx dx=y ##
  41. B

    Differentiation and Simple Pendulums

    Homework Statement *according to my teacher, the problem can be solved either through differentials or quick algebra, but she prefers differentials as the answer in order for us to get used to Calculus, so that's the route I'd like to take it A pendulum made from a string and small metal ball...
  42. B

    How is implicit differentiation performed in calculus?

    Folks, Differentiate implicitly \phi(x,y)=0 I get: wrt to x \phi_x+\phi_y \frac{dy}{dx} and wrt to y \phi_y+\phi_x \frac{dx}{dy} however I don't know how this is derived \phi_x dx+\phi_y dy=0
  43. hancmarginis

    Simple differentiation problem

    .
  44. B

    MHB Yes, that makes sense! Thank you for explaining it to me.

    Hi Folks, It is been given that differentiation of \phi(x,y)=0 is \phi_{x} dx+ \phi_{y} dy=0 however I arrive at \phi_{x} dx/dy+ \phi_{y} dy/dx=0 via the chain rule. Where \phi_{x}=d \phi/dx etc What am I doing wrong? Thanks
  45. K

    How to Correctly Calculate Partial Differentiation

    Hello Is what I have done calculated here correct? Please correct me if I have done something wrong. Thanks in advance.
  46. S

    Minimizing surface area of a shaker

    Hi, I have an mathematics assignment to do, and I wonder if the topic I have chosen is doable for me. I want to minimize the surface area of a cobbler cocktail shaker, and until now my plan was to get the curve equation for the side of it, and get the area equation from surface of revolution...
  47. PhysicsBoyMan

    Why is the new format necessary before differentiating?

    Homework Statement http://postimage.org/][/PLAIN] click image upload Homework Equations http://postimage.org/][/PLAIN] free image upload The Attempt at a Solution So I wanted to differentiate B(t) by saying B(t) = P(t)(1.05)20-t ln(1.05) Apparently this is the wrong answer. I'm...
  48. D

    Hyperbolic Differentiation: How Do We Differentiate Functions with Exponents?

    Homework Statement Differentiate Homework Equations Chain Rule: dg/dx = du/dx . dv/du . dg/dv The Attempt at a Solution My answer(wrong): Correct answer provided to us(not mine): I understand the correct solution that was provided to us, but what I don't understand is why my method...
  49. Calpalned

    Which is the constant of differentiation?

    When the textbook differentiated with respect to time, I see that the middle term is R(dI/dt). Why can't it be I(dR/dt)? When I differentiate, how do I know which letter to differentiate? 3. The Attempt at a Solution 2. Homework Equations 1. Homework Statement
  50. J

    Rodrigues’ formula of Laguerre

    Homework Statement I need to proof that Rodrigues’ formula satisfies Laguerre differential equation Homework Equations Rodrigues’ formula of Laguerre Laguerre differential equation The Attempt at a Solution first,I have to calculate = I tried to sum both terms and this is what I got...
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