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. B

    Partial differentiation problem, multiple variables (chain rule?)

    Homework Statement if z = x2 + 2y2 , x = r cos θ , y = r sin θ , find the partial derivative \left(\frac{\partial z}{\partial \theta}\right)_{x} Homework Equations z = x2 + 2y2 x = r cos θ y = r sin θ The Attempt at a Solution The textbook says that the equation should be...
  2. J

    Implicit Differentiation: Solving for y' in y^2sin(x)

    Homework Statement Differentiate using implicit differentiation y^2sin(x) Homework Equations I know you need the chain rule and the product rule to solve this The Attempt at a Solution So, it would be: 2yy' + y^2cos(x) Is that correct?
  3. adjacent

    How do I find the gradient of the tangent at a given point on a quadratic curve?

    Homework Statement Find the gradient of the tangent at x on the following curve ##y=3x^2## Homework Equations $$\lim_{\Delta x\rightarrow 0}\frac{f(x+\Delta x)-f(x)}{\Delta x}$$The Attempt at a Solution I know that it's ##6x##. $$\frac{3(x+\Delta x)^2-3x^2}{\Delta x}$$ $$=\frac{3x^2+6x\Delta x...
  4. T

    Differentiation with electricity help

    Homework Statement A circuit consists of 230V supply, a switch, a 2mH inductor and a 12k ohm resistor in series When the switch is closed at time t=o, a current i begins to flow in the circuit: The current is modeled by the following equation: i= v/r (1-e^-Rt/L) Determine the...
  5. J

    Can a repeated integral be simplified into a single integral?

    If a repeated integral can be expressed how an unique integral: https://en.wikipedia.org/wiki/Cauchy_formula_for_repeated_integration So is possible express the nth derivative with an unique differentiation?
  6. Matterwave

    Is Functional Differentiation Applicable to Quantum Field Theory Functionals?

    Hi guys, I'm not sure where to put this question, so I'll just put it here. If a mod knows of a better place, just point me to it, thanks. I'm looking at the functional differentiation equation: $$\left.\frac{dF[f+\tau h]}{d\tau}\right|_{\tau=0}\equiv \int\frac{\delta F[f]}{\delta...
  7. W

    Understanding the Discrepancy in Four-Vector Differentiation in QFT

    Hi all, I'm working on some QFT and I've run into a stupid problem. I can't figure out why my two methods for evaluating i\gamma^\mu \partial_\mu \exp(-i p \cdot x) don't agree. I'm using the Minkowski metric g_{\mu\nu} = diag(+,-,-,-) and I'm using \partial_\mu =...
  8. Matterwave

    Functional differentiation and integration

    Hi guys, I'm trying to study the functional approach to quantization in QFT. The QFT books seem to often "sweep things under the rug" and not be too rigorous when it comes to issues like integral convergence, and the like. So I was wondering if there was a more mathematically rigorous...
  9. J

    Differentiation of coordinate wrt another coordinate

    When I take the differential of y wrt t (being t a parameter (time)) I get the velocity of the y-coordinate, if take the second differential of y wrt t, thus I get the aceleration of the y-coordinate... ok! But what means to differentiate the y-coordinate wrt x-coordinate, or wrt y, or then...
  10. J

    Implicit Differentiation?

    Homework Statement Find the derivative of: x+xy=y^2 Homework Equations So I know you have to differentiate it, and it would be: 1+xyy'=2yy' The Attempt at a Solution Moving the terms with y' to one side: 1+xyy'-2yy'=0 xyy'-2yy'=-1 Factoring out y'...
  11. Saitama

    MHB True/False differentiation problem

    Problem: Let $g(x)$ be twice differentiable function satisfying $g(0)=0$, $g(1)=1$. Then, which of the following is/are correct? A) there exist distinct $C_1,C_2\in (0,1)$ such that $g'(C_1)+g'(C_2)=2$. B) there will be atleast one $C$ such that $g'(C)=1$ for $C\in (0,1)$ C) there will be...
  12. N

    Differentiation of vector function(explanation of solution)

    Homework Statement Show that if the vector function r(t) is continuously differentiable for t on an interval I and |r(t)| = c, a constant for all t \in I, then r'(t) is orthorgonal to r(t) for all t \in I What would the curve described by r(t) look like? The Attempt at a Solution...
  13. J

    Partial and total differentiation

    You can give me a good examples where ##\frac{\partial}{\partial x}## is different to ##\frac{d}{dx}## ?
  14. J

    Partial Differentiation: second partial derivative

    I am not quite sure how \frac{\partial}{\partial u}\left(\frac{\partial z}{\partial u}\right) =\frac{\partial}{\partial u}\left( u \frac{\partial z}{\partial x}+v\frac{\partial z}{\partial y} \right) comes to \frac{\partial z}{\partial x} + u\frac{\partial}{\partial u}\left(\frac{\partial...
  15. G

    Hyperbolic Differentiation

    Homework Statement y=1 / (cos h x), find dy/dx Homework Equations chain rule and coshx=(e^x+e^-x)/2 The Attempt at a Solution
  16. A

    A question about log differentiation

    is necessary to simplified the equation before differentiation? could I use the Quotient Rule without of simplifying ?
  17. G

    How to differentiate 1/y without making a fundamental mistake?

    Problem statement Find dy/dx Revelant equations None Attempt at a solution This is what I got to so far but now I'm stuck... Any hints?
  18. W

    Differentiation under the integral sign

    I have read about this method , and how feynman utilized this method. I like doing integrals for fun, but I can't seem to understand the conceptual idea on how to introduce a parameter into the integral. Can someone , in detail, explain to me how to introduce the parameter into the integral ...
  19. T

    MHB Confusing Implicit Differentiation Problem

    Hi, I have x =(x^2+y^2)^[1/2] I differentiate 1= 1/2 (x^2+y^2)[-1/2] (2x+2yy') So far so good. I try to multiply this out. 1= (2x)/2 (x^2+y^2)[-1/2] + (2yy'/2)(x^2+y^2)[-1/2] I solve for y' y'= 1/{(x (x^2+y^2)[-1/2]} / {y(x^2+y^2)[-1/2] } 1/x (x^2+y^2)[1/2] * 1/y (x^2+y^2)[1/2] The...
  20. P

    Differentiation of inverse trig

    Say we want to differentiate \arcsin x. To do this we put y=\arcsin x. Then x=\sin y \implies \frac{dx}{dy}= \cos y. Then we use the relation \sin^2 y + \cos^2 y = 1 \implies \cos y = \sqrt{1 - \sin^2 y} = \sqrt{1 - x^2}. Therefore \frac{dy}{dx} = \frac{1}{\sqrt{1 - x^2}}. My question is that...
  21. T

    Partial differentiation and partial derivatives

    Homework Statement If ##xs^2 + yt^2 = 1## (1) and ##x^2s + y^2t = xy - 4,## (2) find ##\frac{\partial x}{\partial s}, \frac{\partial x}{\partial t}, \frac{\partial y}{\partial s}, \frac{\partial y}{\partial t}## at ##(x,y,s,t) = (1,-3,2,-1)##. Homework Equations Pretty much those just listed...
  22. L

    Taylor series problem (non-direct differentiation?)

    I attached a picture of the problem from my online HW. I know how to solve the problem through direct differentiation, but that would too long to find the derivatives for this problem, and the problem actually suggests that I find another way. So my question is, what's the best way to solve this?
  23. Nemo's

    Differentiation inverse of a hyperbolic function

    Homework Statement d/dθ csc-1(1/2)^θ = ? Homework Equations d/dx csc-1(x) The Attempt at a Solution I don't know how to deal with the exponent θ
  24. lfdahl

    MHB Partial differentiation of an integral

    Hello MHB members and friends!(Callme) An economy student asked me, if I could explain the following partial differentiation: \[\frac{\partial}{\partial C(i)}\int_{i\in[0;1]}[C(i)]^\frac{\eta - 1}{\eta}di =\int_{j\in[0;1]}[C(j)]^\frac{\eta - 1}{\eta}dj\frac{\eta -...
  25. MarkFL

    MHB Gan's questions at Yahoo Answers regarding differentiation

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

    Partial Differentiation Identity Problem

    Homework Statement Show that a relation of the kind ƒ(x,y,z) = 0 then implies the relation (∂x/∂y)_z (∂y/∂z)_x (∂z/∂x)_y = -1 Homework Equations f(x,y) df = (∂f/∂x)_y dx + (∂f/∂y)_x dy The Attempt at a Solution I expressed x = x(y,z) and y = y(x,z) then found dx and...
  27. applestrudle

    Partial differentiation question?

    Homework Statement z = x^2 +y^2 x = rcosθ y = rsinθ find partial z over partial x at constant theta Homework Equations z = x^2 +y^2 x = rcosθ y = rsinθ The Attempt at a Solution z = 1 + r^2(sinθ)^2 dz/dx = dz/dr . dr/dx = 2(sinθ)^2r/cosθ = 2tanθ^2x...
  28. G

    How do I compute the following differentiation by chain rule?

    How do I compute the following differentiation by chain rule? \frac{d}{d\lambda}(\lambda^{-1}\phi(\lambda^{-1}x)) It is not a homework, but I can't figure out the exact way of getting the answer -\phi(x)-x^{s}\partial_{s}\phi(x)
  29. K

    MHB Intermediate Value Thm for Five-Point Formula

    I have a specific, for-learning-sake-only question on how the author of this link: http://www.math.ucla.edu/~yanovsky/Teaching/Math151A/hw5/Hw5_solutions.pdf gets past the details of the Intermediate Value Theorem on the following paragraph. If someone could fill in the details for me, it...
  30. patrickmoloney

    How to Apply Partial Differentiation to V=f(x²+y²)?

    Homework Statement let V=f(x²+y²) , show that x(∂V/∂y) - y(∂V/∂x) = 0 Homework Equations The Attempt at a Solution V=f(x²+y²) ; V=f(x)² + f(y)² ∂V/∂x = 2[f(x)]f'(x) + [0] ∂V/∂y = 2[f(y)]f'(y) I'm sure I've gone wrong somewhere, I have never seen functions like this...
  31. H

    Momentum operator as differentiation of position vector

    Is it possible to take momentum operator as dr/dt (r is position operator)? If not, why?
  32. Y

    Differentiation in spherical coordinates.

    1) If u(r,\theta,\phi)=\frac{1}{r}, is \frac{\partial{u}}{\partial {\theta}}=\frac{\partial{u}}{\partial {\phi}}=0 because u is independent of \theta and \;\phi? 2) If u(r,\theta,\phi)=\frac{1}{r}, is: \nabla^2u(r,\theta,\phi)=\frac{\partial^2{u}}{\partial...
  33. J

    Differentiation with respect vector

    Helow! For a long time I aks me if exist differentiation/integration with respect to vector and I think that today I discovered the answer! Given: f(\vec{r}(t)) So, df/dt is: \bigtriangledown f\cdot D\vec{r} But, df/dt is: \frac{df}{d\vec{r}}\cdot \frac{d\vec{r}}{dt} This means that...
  34. H

    Need help quik with this differentiation

    Homework Statement Homework Equations \frac{d}{dx} The Attempt at a Solution i couldn't do it because we didnt learn this type of question
  35. N

    Need help understanding a differentiation

    I'm working my way through a solution of a problem and am confused on a step where a differentiation is performed. I'm sure I'm just forgetting some kind of rule, but I've been perusing my textbook and can't seem to figure out what I'm missing. Here's the step I'm talking about: Note that...
  36. A

    MHB Trouble with Solving a Partial Differentiation Problem?

    I got x = (u2 - v2) / u y = (v2 - u2) / v I differentiated them w.r.t u & v respectively & solved the given equation but I'm not getting the answer which is 0. Please view attachment for question!
  37. F

    Complicated implicit multivariable differentiation problem

    Homework Statement Given that the surface x^{6}y^{5}+y^{4}z^{5}+z^{9}x^{7}+4xyz=7 has the equation z = f(x, y) in a neighborhood of the point (1, 1, 1) with f(x,y) differentiable, find: \displaystyle\frac{\partial^{2} f}{\partial x^{2}}(1,1) = ? Homework Equations The Attempt at a Solution...
  38. MarkFL

    MHB Angelina Lopez's Calculus Questions on Differentiation

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

    Partial differentiation with 3 variables

    Given a function: z(x,y) = 2x +2y^2 Determine ∂x/∂y [the partial differentiation of x with respect to y], Method 1: x = (z/2) - y^2 ∂x/∂y = -2y Method 2: ∂z/∂x = 2 ∂z/∂y = 4y ∂x/∂y = ∂x/∂z X ∂z/∂y = (1/2) X 4y = 2y One or both of these is wrong. Can someone point out...
  40. MarkFL

    MHB Robert's questions at Yahoo Answers regarding differentiation

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

    Find the Derivative of y2 = 2x + 1How can I find the derivative of y2 = 2x + 1?

    Homework Statement Hello, I missed the class where we were introduced to implicit differentiation so have been catching up this evening. I think I have it, but please could you check my working? Thanks! Find the derivative of y2 = 2x + 1 \frac{d}{dx}([f(x)]^{2}) = \frac{d}{dx}([2x])...
  42. P

    Implicit differentiation and related rates

    Homework Statement The spherical head of a snowperson is melting under the HOT sun at the rate of -160 cc/h (cubic centimetres per hour.) Find the rate at which the radius is changing when the radius r=16. Use cm/h for the units. (The volume of a sphere is given by V= 4π⋅r^3/3.) I have...
  43. P

    Regarding logarithmic differentiation

    Thank you for viewing my thread. I have been given the following steps for logarithmic differentiation: 1. Take natural logarithms of both sides of an equation y = f(x) and use the Laws of Logarithms to simplify. 2. Differentiate implicitly with respect to x. 3. Solve the resulting equation for...
  44. C

    MHB Implicit differentiation with exponential function

    find dy/dx: exy+x2+y2= 5 at point (2,0) I'm confused with finding the derivative with respect to x of exy. this is what I did so far for just this part: exy*d(xy)/dx exy*(y+x*dy/dx) do I need to put the parentheses on here? I thought so because that is the part where I used the product rule...
  45. Y

    Verify partial differentiation.

    I just want to verify For Polar coordinates, ##r^2=x^2+y^2## and ##x=r\cos \theta##, ##y=r\sin\theta## ##x(r,\theta)## and## y(r,\theta)## are not independent to each other like in rectangular. In rectangular coordinates, ##\frac{\partial y}{\partial x}=\frac{dy}{dx}=0## But in Polar...
  46. M

    Trigonomentry, differentiation + equation.

    I have another two problems I find difficult. They both involve trigonometry, so I thought I could fit both under the same post. Also, if possible, I'd like some help in regards to confirming that one problem I've solved is done correctly. Homework Statement First, the derivative. Find y'...
  47. Y

    Question on differentiation.

    ##r^2=x^2+y^2\;\Rightarrow \; 2r\frac{dr}{dx}=2x\;\Rightarrow\; \frac{dr}{dx}=\frac{x}{r}## Then is it true ##\frac{dx}{dr}=\frac{r}{x}##? I am not sure this is correct as r^2=x^2+y^2\;\Rightarrow \; 2r=2x\frac{dx}{dr}+2y\frac{dy}{dr}
  48. B

    Checking My Method For Differentiation

    Homework Statement Differentiate the following with respect to x y = \frac{4}{x^{3}} + \frac{x^{3}}{4}The Attempt at a Solution So the problem here is really getting this into a form that is easy to differentiate and i'd just like to show what I'm doing before I go ahead and do the rest of...
  49. A

    Confusion regarding use of differentiation and unit vectors

    Hey, everyone. I am going to post a question—but it's not the question I need help with. It's something deeper (and way more troubling). Consider a particle of mass m subject to an isotropic two-dimensional harmonic central force F= −k\vec{r}, where k is a positive constant. At t=0, we...
  50. MarkFL

    MHB Duncan G's Questions on Implicit Diff. & Related Rates

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