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. C

    Differentiation problem square root function

    I'm on mobile so I can't use latex. Differentiate: g(x)=√(4-x^4) , x is a set of [-√2, √2] and determine the domains. So I got the derivative which is, g'(x)=(-4x^3) ^1/2 What should I do with the -+√2 ? I don't know what to do next
  2. K

    Questions on connections and covariant differentiation

    The question is in the pdf file,thank you!:smile: M is a Riemannian manifold, $\vdash$ is a global connection on M compatible with the Riemannian metric.In terms of local coordinates $u^1,...,u^n$ defined on a coordinate neighborhood $U \subset M$, the connection $\vdash$ is...
  3. K

    Partial differentiation -higher order

    Homework Statement The determinant J (f,g/u,v) =|∂f/∂u ∂f/∂v ∂g/∂u ∂g/∂v |: if z = f(x,y) and g(x,y) = 0, show that dz/dx = ∂f/∂x*∂g/∂y - ∂f/∂y * ∂g/∂x/∂g/∂y = 1/ ∂g/∂yJ(f,g/x,y) Homework Equations...
  4. K

    Partial Differentiation - The Chain Rule

    Homework Statement Calculate ∂f/∂s + ∂f/∂t at s = 2, t = -1. Given: f = f(x,y) x = s - t y = s2 + t2 ∂f/∂x (3,5) = 0.06170 ∂f/∂y (3,5) = 0.06170 Homework Equations ∂f/∂s = ∂f/∂x * ∂x/∂s + ∂f/∂y * ∂y/∂s ∂f/∂t = ∂f/∂x * ∂x/∂t + ∂f/∂y * ∂y/∂t The Attempt at a Solution...
  5. S

    What is the partial derivative of T with respect to time?

    Homework Statement Hello all, New to partial derivatives. I was wondering if someone could look over my work and determine if my final step is as far as I can take the proble (ie. that will be my solution). Thanks in advance. Let the temperature of a 2D domain in polar coordinates (r...
  6. S

    What exactly is integration and differentiation?

    in a non mathematical sense? My maths isn't very good which is why I need some simple explanation of what they are. What does integration do? What is its purpose and how does its purpose apply to the natural world? I know differentiation is the opposite process but what is it exactly...
  7. Q

    Differentiation concept problem

    Homework Statement i am suddenly stuck when differentiating. are my concepts right? if we integrate cosx/sinx, then since cosx is the differentiated form of sinx, then integrating d(sinx)/sinx = ln|sinx| so now, if i have : integrate z/(1-z2)1/2 since z is the differentiated form of the...
  8. S

    Differentiation - finding equation of normal to curve

    Homework Statement Find the equation of the normal to the curve y=(6x+3)^(1/2) at the point for which x=13. Homework Equations dy/dx=dy/du*du/dx y-y1=m(x-x1) The Attempt at a Solution y=(6x+3)^(1/2) dy/dx=1/3(6x+3)^2 gradient of normal = -3(6x+3)^2 at x=13...
  9. N

    Efficient Differentiation of Hyperbolic Integrals

    Hello again :) I get the feeling I'm missing some kind of 'trick', as this is proving a very difficult question :( I'll write out my frustration below; Homework Statement Find f'(x) if f(x) = \int^{cosh(x^{2})}_{0} tanh(t^2)dt Homework Equations --- The Attempt at a Solution My idea was...
  10. I

    Does the derivative df/dg of the function f(g) exist and what does this mean?

    Homework Statement when is this statement true : the derivative df/dg of the function f(g) exists what does this mean exactly? Homework Equations The Attempt at a Solution does it mean- 1. df/dg represents the rate of change of f with respect to g at any given value...
  11. C

    Second derivative using implicit differentiation

    Homework Statement x^6 + y^6 = -6 I have to prove that y'' = 30x^4/y^11 Homework Equations The Attempt at a Solution Using implicit differentiation: 6x^5 + 6y^5 dy/dx = 0 6y^5 dy/dx = -6x^5 dy/dx = -x^5/y^5 Quotient Rule: [(y^5)(-5x^4) - (-x^5)(5y^4 dy/dx)] /...
  12. J

    How Do You Find the Critical Point of f(x) = e^x - 5x^2 - ln(x)?

    Homework Statement I'm stuck halfway in my differentiation. The question is: Suppose f(x) is the following function when x > 0, find the x-coordinate of the critical point of f(x). Homework Equations Equation = f(x) = e^x - 5x^2 - ln(x) The Attempt at a Solution I solved for...
  13. D

    Partial Differentiation with Einstein Notation

    Hi there, I'm writing a research paper and have hit a roadblock, (wikipedia did not help) and one of my collaborators sent me an e-mail that I do not understand. I am attempting to find when the following functional is stationary: T = \int\limits_{\lambda_{1}}^{\lambda_{2}}...
  14. A

    Implicit differentiation, find y''

    the problem is to find y'' or d2y / d2x the equation is y2 = x2 first i found the first derivative dy/dx = 2x / 2y = x / y then i found the second using the quotient rule and got y'' = (y - x(dy/dx)) / y2 i plugged in y' into y'' and got y'' = (y - (x2/y)) / y2 but then I am...
  15. N

    A question in logarithmic differentiation

    In most of exercises of textbooks when ask me to differentiate f using logarithmic differentiation some time f(x) = 0 for some values of x , so I I used logarithmic Differentiation for all x in domain of f , such that f(x) not equal zero. then prove using the definition directly that for...
  16. R

    Covariant vector differentiation problem with kronecker delta?

    I'm having trouble understanding the proof/solution below (please see photo, I also wrote out the problem below). I highlighted the part of my problem in red (in the picture attached). Basically I'm not sure what identity they use to get the Kronecker delta after differentiating or whether they...
  17. R

    Automatic differentiation for numerical integration

    I've written a Levenberg-Marquardt nonlinear optimization routine that employs the reverse-mode automatic differentiation algorithm for building the Jacobian. So far it has worked marvelously for me. However, now I have to use functions that contain integrals that cannot be analytically taken...
  18. X

    Differentiation - chain and product rule.

    It's been years since I've done maths properly so I'm rusty with it. I'm helping out a colleague at work who is studying maths for an OU course. Homework Statement Part 1: Differentiate function. f(x) = e^(0.5x+cos(x)) Part 2: Use answer from part 1 to show. g(x) =...
  19. Q

    Differentiation - Product Rule

    Homework Statement In general I havn't had problems using the differentiation rules until I came on this question, I'm probably doing something stupid any help is handy. Plugged it into an online differentiation solver and it comes up with (x^2-1)/(x^2) which I am getting nowhere near to in my...
  20. H

    Commutativity of differentiation in a special case

    Problem I'd like to prove \frac{d}{dt}[\frac{\partial}{\partial{x}}f(x(t),y(t),t)]=\frac{\partial}{\partial{x}}[\frac{d}{dt}f(x(t),y(t),t)]. Attempt \begin{equation*}\begin{split} \frac{d}{dt}[\frac{\partial}{\partial x}f(x(t),y(t),t)]=\frac{d}{dt}\lim_{\epsilon\to...
  21. G

    Grade 12 Calculus Problem - Differentiation and Division

    Homework Statement Let p be a polynomial function with p(a)= 0 =p'(a) for some real a. Which of the following must be true? A) p(x) is divisible by x+a B) p(x) is divisible by x^2+a^2 C) p(x) is divisible by x^2-a^2 D) p(x) is divisible by x^2+2ax+a^2 E) p(x) is divisible by x^2-2ax+a^2...
  22. C

    MATLAB Differentiation in Script Matlab

    How might I make my script perform differentiation on a user-defined function? I also want the function and its derivative (in the form of a function) to be applied throughout the script, say in the forms of f and f' respectively, which I believe requires str2func. Example: The user is...
  23. A

    Differentiation Problem about a hyperbolic function

    Homework Statement How could one apply differentiation formulas on this one: \partial^{2}\left(2sinh(nx)\div\sqrt{sinh(2L)-2L}\right)\div\partial x^{2} Homework Equations The Attempt at a Solution is this differentiation formula enough to differentiate:
  24. T

    Finding extreme values by partial differentiation.

    Homework Statement I sat my calculus exam at the end of june and of the questions on the paper required us to find the extreme values of the following equation: g\left(x,y\right) = \left(x-1\right)\left(y-1\right)\left(x^{2} + y^{2} -2\right) The Attempt at a Solution So i get...
  25. S

    Partial differentiation when the variable of integration is different

    Consider the partial differential of Q to the power of n w.r.t. x. How would you rearrange this expression so that it contains a partial derivative of Q w.r.t. x?
  26. O

    Very Quick Differentiation Question

    First I attempted to ipmlicitly differentiate c2 = a2 + b2 -2abcos(theta) da/db I almost got the correct solution according to MIT's key, however I missed one part. The cos from the original function remained cos, and I had differentiated it to -sin. I'm just wondering why it...
  27. P

    What is the Solution to the Differentiation Problem (3x+2)^5.(x+1)^-2?

    Homework Statement (3x+2)^5.(x+1)^-2 Homework Equations dy/dx = dy/du . du/dx The Attempt at a Solution y=(3x+5)^5 . (x+1)^-2 u = 3x + 5 , du/dx = 3 v = u^5 , dv/du = 5u^4 = 15(3x+5)^4 u = x + 1 , du/dx = 1 v = u^-2 , dv/du = -2u^-3 -2(x+1)^-3 dy/dx = 15(3x+5)^4 ...
  28. C

    Partial differentiation question?

    The coefficient of rigidity n of a wire of length L and uniform diameter is given by: n = AL/d^4 where A is a constant...If errors of +- 0.25% and +-1% are possible in measuring L and d respectively, find the maximum possible error in the calculated value of n... how do i do this...
  29. A

    Implicit Differentiation: Finding d^2y/dx^2 at a Given Point

    Homework Statement find the d^2y/dx^2 if y^3 + y = 2 cos x at the point (0,1) Homework Equations The Attempt at a Solution my dy/dx = (-2 sin x)/(3y^2 + 1) I don't know how to find d^2y/dx^2? And when and how will I use the oint (0,1)?
  30. L

    Derivative implicit differentiation problem

    Homework Statement Consider the curve satisfying the equation 2(x+1)^(tanx)=(y^2)cosx+y and find dy/dxHomework Equations (tanx)'=sec^2x (lnx)'=1/xThe Attempt at a Solution I've tried taking the natural log of both sides and then taking d/dx of both sides but something seems to go wrong with...
  31. Femme_physics

    What is the use of implicit differentiation in solving complex equations?

    http://img838.imageshack.us/img838/8007/given01.jpg http://img220.imageshack.us/img220/52/given2r.jpg Actually that should be the square root of -2X
  32. B

    Related rates and implicit differentiation

    Homework Statement A plane flying with a constant speed of 300 km/h passes over a ground radar station at an altitude of 1 km and climbs at an angle of 30 degrees. At what rate is the distance from the plane to the radar station increasing a minute later? Homework Equations a2+b2=c2The...
  33. B

    Mathematical Induction: Power Rule for Differentiation

    Homework Statement Prove that \frac{d}{dz}z^n = nz^{n-1}\;\;\; \forall n\in\mathbb{N} using the Product Rule for differentiation and mathematical induction. Homework Equations \frac{d}{dz} f(z) = \lim_{\Delta z\to 0} \frac{f(z+\Delta z) - f(z)}{\Delta z} \frac{d}{dz}[f(z)g(z)] = f\,'(z)g(z) +...
  34. P

    What is wrong with this differentiation?

    Homework Statement Find dy/dt, given: y=x^2-5x+1 x=s^3-2s+1 s=\sqrt{t^2+1} 2. The attempt at a solution I am trying to use the chain rule for the case where y is a function of x, x is a function of s and s is a function of t, like below...
  35. N

    Trouble With Understanding Implicit Differentiation

    I don't think I fully understand implicit differentiation. I have read my textbook and watched many videos, and I think I will get an A on my test on this solely by memorizing the rules, but I would really like to understand this topic. From what I know, you are supposed to use implicit...
  36. 1

    How to Treat Y When Differentiating Implicitly?

    Homework Statement x^{3}y + y^{3}x = 30 Homework Equations - The Attempt at a Solution My understanding is that I'm supposed to take the derivative of each side and try to solve for y'. But, I don't know how to treat the y when I am differentiating it, to a power or whatever...
  37. S

    Matrix dimensions are not matching after differentiation

    I'm doing some work with neural networks lately and I'm having trouble with this seemingly simple equation. The equation describing the network is: y = \psi(W3 x \psi(W2 x \psi(W1 x I))) Where: y (scalar) is the output value W1 (2x2 matrix) are the 1st layer weights W2 (2x2 matrix) are...
  38. D

    Is there a new way to calculate derivatives of factorials?

    I think I have found a formula for finding Successive derivatives of factorials, though it may have been found already. I have attached it to this post.
  39. D

    Differentiation of a Quotient check

    Homework Statement S = (8x^2 - 7x + 125)/(8x+7) Where the value of x is unknown The Attempt at a Solution u = 8x^2 - 7x + 125 du/dx = 16x - 7 v = 8x + 7 dv/dx = 8 ds/dx = (v*du/dx - u*dv/dx)/v^2 = (8x+7*16x-7 -...
  40. D

    Differentiation of a product check

    Homework Statement s = 8sin(125t)e^-7t Where the value of t is unknown The Attempt at a Solution u = 8sin(125t) du/dt = 1000cos(125t) v = e^-7t dv/dt = -7e^-7t ds/dt = v*du/dt + u*dv/dt = (e^-7t *...
  41. QuarkCharmer

    Implicit Differentiation, and the Chain Rule

    Homework Statement Use implicit differentiation to find dy/dx 2x^3+x^2y-xy^3 = 2 Homework Equations Chain Rule et al. The Attempt at a Solution My questions is this. When deriving something like xy^3, apply the product rule to get 1y^3 + x\frac{d}{dx}y^3 I am confused on...
  42. dkotschessaa

    Logarithmic Differentiation Problem

    The problem I am having with these is that I'm sometimes not sure whether to begin differentiating first, or to start taking logarithms - and whether the order changes the outcome For example: Find the equation of the tangent line to the curve at the given point. y= \frac{(e^x)}{x}...
  43. A

    Can you find the zeros of a quadratic equation using differentiation?

    Given an equation in the form 0 = ax2 + bx + c, why is it not possible to simply differentiate both sides, and produce 0 = 2ax + b, and solve for x, instead of going through the drudgery of the quadratic equation? My knowledge of calculus tells me that it is because 0 = ax2 + bx + c is not a...
  44. W

    Correct differentiation identity? (tensors, vectors)

    Hello, I'm working on some problems and I want to pose the following, though I am not completely sure it is correct. Can somebody point me to some sources on this? I have tried googling myself, but I only found differentiation identities with either just vectors and scalars on the on hand, or...
  45. F

    Implicit Differentiation with Mathematica

    Homework Statement I tried using D[x = y - y^2, x, NonConstants -> {y}] and it keeps telling me that y - y^2 is not a valid variable.
  46. W

    Website title: Partial Differentiation for f(x,y)=(3x^2+y^2+2xy)^1/2

    Find ∂fxand ∂fy for: f(x,y)=(3x2+y2+2xy)1/2 i tried using the chain rule and said f(x,y) = u1/2 then ∂fu = 1/2u-1/2, ∂ux = 6x + 2 and ∂uy=2y+2 ∂fx = 1/2(3x2 + y2 + 2xy)-1/2(6x + 2) ∂fy = 1/2(3x2 + y2 + 2xy)-1/2(2y + 2) im not sure if this is correct as i don't know if I am doing the ∂ux and...
  47. S

    Questions involving implicit differentiation,

    Homework Statement Q1. using implicit diff to find dy/dx when x^2 y + 6xy^2 = 5x-2 Q2. Find max and min values of y= x^3 -3x^2 -6x + 7 on the interval -3<=x<=5 Q3.Find the exact values of the x coordinate of the points of inflexion on the graph of y = 2x^4 +3x^2 +x +5 Q4. a red car is...
  48. P

    Differentiation of function x^x

    Just wondering if I have done this correctly? Homework Statement Differentiate: x^{sin3x} The Attempt at a Solution x^{sin3x}=e^{sin(3x)ln(x) Employing chain rule. y=e^{u} u=sin(3x)ln(x) dy/dx = e^{u}\times(sin(3x)/x + 3ln(x)cos(3x)) Final Solution? = dy/dx =...
  49. P

    Calculus problem involving implicit differentiation.

    Good afternoon, This is not actually a homework question; it's for self-study. I'm reading a Calculus book, and one of its exercises asks the following: If xnym = (x+y)n+m, show that xDxy = y (where Dxy is the derivative of y with respect to x). The only way I could think of to get the correct...
  50. M

    Is the derivative of y = x^i equal to ix^{i-1} and is y always real?

    Hello guys Let y = x^i x is real, i imaginary, then is it right to say: y' = ix^{i-1} and must y be real?
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