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).

View More On Wikipedia.org
Recent contents Top users
  1. D

    Limit similar to differentiation

    Homework Statement f a differentiable real valued function lim h - > 0 of (f(x + ah) - f(x + bh))/h where a,b real numbers Homework Equations definition of derivative lim h-> 0 of (f(x+h) - f(x))/h The Attempt at a Solution I've picked several functions like x^2 and 1/2x...
  2. K

    Proving one Differentiation results to another

    Homework Statement I need in proving that the derivative (d^{n}/dx^{n})(sin4x + cos4x) = 4n-1 cos(4x + n\pi/2) The Attempt at a Solution I understand implicit differentiation in basic problems but I get stump with the n exponent in the differentiation symbol; am I suppose to treat it as...
  3. D

    Numerical Differentiation: Difference approximation on numerical data

    Homework Statement I am given a table of data derived from experiment. A force (F) is applied to a spring and the extension (x) is measured and recorded. An additional column of data for the derivative (dF/dx) is also provided. Here is the data: x(m) F(kN) df/dx (kN/m) 0.0...
  4. K

    Implicit Differentiation and coordinates

    Homework Statement Find the coordinates of the point in the first quadrant at which the tangent line to the curve x3-xy+y3=0 is parallel to the x-axis. SO: x= + y= + mtan=0 Homework Equations \frac{dy}{dx}=m_{tan} The Attempt at a Solution \frac{dy}{dx}=\frac{y-3x^{2}}{3y^{2}-x}=0 After I...
  5. R

    Differentiation of natural logarithms

    I encountered a proof problem when I was reading up on the derivatives of natural logarithms' section. It gave a rule which said this : \text{For } a >0 \text{ and } a\ne 1 \text{,}\\\frac{d}{dx}(a^{u}) \ = \ a^{u} \ \ln{a\frac{du}{dx}} To prove it on my own, I made a few identities: a^{u}=y...
  6. K

    Differentiation & composite functions (2)

    Suppose we are given that d --F(y) = f(y) dy Then is it true that dF(h(u)) -------- = f(h(u)) dh(u)/du ? du Why or why not? In particular, I don't understand how to get the red part... Thanks for explaining!
  7. K

    Differentiation & composite functions

    What is the actual meaning of the notation of df[g(x)] ------- dx Here do we actually differentiate f with respect to x first and then evaluate it at g(x), or do we first evaluate f at g(x), then differentiate it with respect to x? Does the order matter? df --[g(x)] dx d...
  8. N

    2 Problems. 1 regarding implicit differentiation

    1) A particle is moving along the curve y=3sqrt{3x+3}. As the particle passes through the point (2, 9), its x-coordinate increases at a rate of 2 units per second. Find the rate of change of the distance from the particle to the origin at this instant. 2) Use implicit differentiation to find...
  9. C

    What Mistakes Did I Make in My Calculus Homework?

    Homework Statement Hello guys. I had to do some test corrections for my AP Calculus AB class. I have completed all of them besides the four below. Can anyone tell me where I go wrong? 1. Differentiate y = (1+cosx)/(1-cosx) dy/dx = [(1-cosx)(sinx)-(1+cosx)(sinx)]/(1-cosx)^2...
  10. N

    How do I find the slope of a tangent line using implicit differentiation?

    Homework Statement Use implicit differentiation to find the slope of the tangent line to the curve 4x^2-3xy+1y^3=26 at the point (3,2) The Attempt at a Solution I attempted the problem and i came up with dy/dx= (-8x+4)/(3y^2) which is wrong. Need some help with this.
  11. D

    Implicit Differentiation w/ trig functions check

    Homework Statement Determine dy/dx when y*sin(x2)=5 The Attempt at a Solution y*2xcos(x2) dx/dx + sin(x2)*1 dy/dx = 0 2xy cos(x2)*dy/dx = -sin(x2) dy/dx = -sin(x2) / 2xy cos(x2) dy/dx = -2xy tan(x2)
  12. D

    Check request: Implicit Differentiation

    Homework Statement Find the value of dy/dx at x=2 when x2+xy=5 The Attempt at a Solution To find y: 22+2y=5 y=1/2 To find dy/dx: 2x(dx/dx)+x(dy/dx)+y(dx/dx)=0 2x+x(dy/dx)+y=0 (dy/dx)=(-2x-y) / x Plug in y and x: dy/dx=-2(2)-(1/2) / 2 dy/dx=-9/4 when x=2
  13. B

    Differentiation questions

    Homework Statement Find dy/dx for: a) xsin(xy^2) - ln(x/y) = y b) x = 3cos(a), y = 2sec(a). simplify then find dy/dx when a = pi/3 Homework Equations The Attempt at a Solution I've done both of them, was just hoping someone could check I've done things correctly. I'm...
  14. S

    Partial Differentiation of an expression.

    Homework Statement Find the partial of z with respect to x keeping r constant. Homework Equations z=x2+y2 x= rcos(t) y= rsin(t) The Attempt at a Solution= r^2(cos(t))^2 + r^2(sin(t))^2 use product rule on "x" and hold r and y constant = [0(cos(t))^2 + r^2(2cos(t))(-sin(t)))] + 0...
  15. S

    Differentiation (Trig Function)

    Homework Equations Take the second derivative of: cos(x^2) The Attempt at a Solution cos(x^2) dy/du = -sin(u) du/dx = 2x dy/dx= -2xsin(x^2) I don't know how to begin taking the derivative of this a second time...
  16. S

    Inequality with Differentiation

    Homework Statement Let p > 1, and put q = p/(p-1), so 1/p + 1/q = 1. Show that for any x > 0, y > 0, we have xy <= xp/p + yq/q, and find the case where equality holds. Homework Equations The Attempt at a Solution This is in the differentiation chapter of my analysis book (Browder)...
  17. C

    Re: differentiation of fractional and negative powers

    Hi ! Im having a problem with a question! I need to differentiate the equation 1/ root of (3x^2 + 2) ! Using the formula (f(x+delta) - f(x)) / delta ! Your help would be appreciated!
  18. G

    Implicit Differentiation Check

    Homework Statement just a check, in Implicit Differentiation if you have let's say (x2+y2)2 would you get 2(x2+y2)(2x+2y(dy/dx)) or would it go out of the whole function in the chain rule and be 2(x2+y2)(2x+2y)(dy/dx) much appreciated.
  19. G

    Implicit Differentiation: Finding dy/dx for a Given Equation

    Homework Statement Implicit Differentiation: I Was given the equation find dy/dx: (3x3y2 + 7x) (x2y3 + 3xy)- The Attempt at a Solution Ok, i know i have to use the product rule on top, and on bottom and the quotient rule for the fraction so... if i set s = 3x3 t = y2 u = (3x3y2 +...
  20. S

    Difference between differentiation and partial differentiation

    g = GM/r^2.. since g is an acceleration, Can g be written like this?...g = dv/dt differentiation of velocity..Or partial derivative ∂v/∂t...is this correct...wat is the difference between differentiation and partial differentiation..can somebody explain me which is correct...
  21. L

    Finding the Derivative of a Logarithmic Function with a Variable Exponent

    Another problem I'm not sure of :( find \frac{dy}{dx} for the function xy^{2} + x lnx = 4y my answer y^{2} + x2y \frac{dy}{dx} + lnx + x (1/x) \frac{dy}{dx} = 4\frac{dy}{dx} x2y \frac{dy}{dx} + \frac{dy}{dx} - 4\frac{dy}{dx} = -y ^{2} - lnx \frac{dy}{dx} ( x2y - 3) =...
  22. A

    Solving Practical Differentiation & Integration Equations

    Dear all I am searching the materials that is related with practical problems. Particularly differentiation and integration equations How does one get into solve to use this equations... Also what are the applications,results how much accuracy with practical ...etc Practical books or...
  23. L

    Use implicit differentiation to find dy/dx [Answer check]

    Use implicit differentiation to find \frac{dy}{dx} for xy^{2} – yx^{2} = 3xy i've answered the question but i think I'm doing it wrong any help is appreciated! x(2y)\frac{dy}{dx} – y(2x) = 3xy 2xy \frac{dy}{dx} – 2yx = 3xy 2xy\frac{dy}{dx} = 5xy \frac{dy}{dx} = \frac{5xy}{2xy}...
  24. J

    Implicit differentiation solving a function

    Im trying to solve this function, that is part of a larger equation: \frac{d}{dx} xe^y do I need to get rid of the x term so the y term is dy/dx?
  25. J

    Integration is the inverse process of differentiation

    Hi everyone, I know that integration is the inverse process of differentiation, and that the definite integral is defined as: \int_{a}^{b} f(x) dx = \lim_{n \to \infty} \sum^{n}_{i = 1} f(x_i) \Delta x assuming that the integrand is defined over the interval [a,b]. My question is: Why is...
  26. J

    Solving a Calculus Problem with Implicit Differentiation

    Heres another problem I was working on... http://img141.imageshack.us/img141/2318/calc2qg4.jpg Im trying to find dy/dx using implicit differentiation...my algebra is a bit rusty...but I am trying to make sure I am on the right track...
  27. E

    Solving for Integral with Partial Differentiation

    Do you guys know if it's possible to solve for the following integral l(t)=∫ {a+ [b+cL(t)+exp^L(t)]/d } dt where a, b, c and d are constants and the derivative of L(t) is l(t). Thanks in advance!
  28. G

    Differentiation of Piecewise Functions

    how do you differentiate these equations: f(x) = x^2 x < 3 x + 6 x >= 3 2. f(x) = abs(3x^2 - 6) 3. f(x) = abs(abs(x) - 1) Thank your for your help.
  29. T

    Help With Partial Differentiation & Integration

    I know I should know this... it looks so ridiculously easy. In the course of getting d'Alembert's wave equation solution, we get the following equation: 2cp'\left(x\right)=cf'\left(x\right)+g\left(x\right) The primes are derivatives wrt t. Then we re-order the equation and "integrate the...
  30. T

    Query regarding implicit differentiation

    Homework Statement Use implicit diff to find partial x and partial y if x² + y² + z² = 3xyz The Attempt at a Solution firstly with partial x... 2x + 2z(∂z/∂x) = 3yz + 3xy(∂z/dx) 2x - 3yz = 3xy(∂z/dx) - 2z(∂z/∂x) 2x - 3yz = (3xy - 2z)(∂z/dx) (2x - 3yz)/(3xy - 2z) = (∂z/dx)...
  31. R

    Solving Differentiation Help: Find Time When Acceleration = 0

    Differentiation Help! Homework Statement A particle is moving along a straight line so that, at time t seconds after leaving a fixed point O, its velocity vms-1 is given by v=10sin(1/2 t). Find the time when the acceleration, given by dv/dt, is first zero. Homework Equations sinx...
  32. R

    When is the derivative of a function defined using implicit differentiation?

    Hello! I need some help here please for ppl who are familiar with implicit differentiation. Use implicit differentiation to find dy/dx, in each case say where it is defined; a) y^5 +x^2 y^3 = 1+xy b) y= \frac{x^{3/2}\sqrt{7x^2 +1}}{sin(x) e^{3x^2 + 2x}}, x \neq n\pi n \in Z...
  33. P

    Proving Formula in Vector Differentiation

    1. The problem statement The formula that must be proven is: d (A∙B) = A∙dB + dA∙B du du du 2. The attempt at a solution When I substitute the left side of the equation to the general formula of vector differentiation...
  34. F

    Confusing chain differentiation rule

    If I have a function f from RxR to R, and a function g from RxR to RxR. What are the partial derivatives of the composition f(g)? I end up multiplying the derivative of f with g, but g is a vector? The partial derivative should have its image in R.
  35. N

    Dot Product Differentiation question

    If I differentiate two unit vectors, one with respect to the other, would it just be the dot product between the two vectors (namely the cosine of the angle between them)? I don't understand the physical meaning of the result...
  36. A

    What are some helpful tips for understanding derivatives?

    Hey all- I typed up this little cheat sheet to help me with my learning of derivatives so I though someone else might want to use it for reference. I plan to add to it some examples as well as log and e rules. I will keep you updated if there is any interest in those as well. Enjoy!
  37. A

    Differentiation Of Inverse Function

    Homework Statement \frac{\mathrm{d}\left(\frac{1}{a}\tan ^{-1} \left(\frac{x}{a}\right)\right)}{\mathrm{d}x}2. The attempt at a solution Let y = \frac{1}{a}\tan ^{-1} \left(\frac{x}{a}\right) \therefore x = a \tan \left(ay\right) Differentiate with respect to x \rightarrow 1 = a \sec ^2...
  38. snoopies622

    Find an Online Differentiator - Wolfram

    Wolfram has a nice online anti-derivative finder here http://integrals.wolfram.com/index.jsp but I didn't find a corresponding one for differentiation. Does anyone know of an online differentiator?
  39. S

    Easy Implicit Differentiation Question

    Homework Statement y^2 = 3x^3 + 2x and y must be positive. Find the normal component of acceleration when: x=3m \dot x = 5ms^{ - 1} \ddot x = 5ms^{ - 2} 2. The attempt at a solution Well my approach would be to differentiate it implicitly twice and solve for {\ddot y}. Then I have...
  40. G

    Differentiation of an exponential with operators (Peskin p.84)

    Does anyone know how to differentiate an exponential, which has an operator in its power? I found it quite a trouble in Peskin's QFT (page 84, formulas (4.17), (4.18)). Here we have these two formulas of Peskin: U\left( t,t_{0}\right)=e^{iH_{0}\left( t-t_{0}\right) }e^{-iH\left(...
  41. D

    How can I solve this implicit differentiation problem?

    so I have a implicit diffentiation problem and was wondering if someone could help me out.. I need to figure out how to get dy/dx=0 so eg if i had dy/dx = 4xy+2x/5y^2 and you want to write this in terms of y, how is this done? is there a trick?
  42. J

    What is Implicit Differentiation and How is it Related to the Chain Rule?

    Could someone please explain to me how implicit differentiation is an application of the chain rule? It would be much appreciated. By the way, if it helps, I'm a junior in high school. Thanks.
  43. L

    Is this the correct answer for a partial differentiation question?

    Homework Statement Find the general solution of y' + (2/x)y = 3/(x^2) The Attempt at a Solution xy' + 2y = 3/x d/dx (x * 2y) = 3/x integrating both sides (using product rule for LHS) I end up with y= (3lnx + C)/2x Then I am supposed to find the solution for which y(2)...
  44. P

    Differentiation and integration as opposites

    Homework Statement Can we say that Differentiation and Integration (in Calculus) are inverse operation to each other? Thx Homework Equations The Attempt at a Solution
  45. J

    What is the Implicit Differentiation of the Equation x+y=1+x^3y^2?

    Homework Statement dy/dx: square root x+y= 1+x^3y^2 Homework Equations chain rule implicit differentiation The Attempt at a Solution 1/2 x+y -1/2 =2x^2y^3 *y'
  46. T

    Finding dV/dt in V=4*L^3 at t=0.1s

    I'm having some trouble with the following question, it was on a test previously and I haven't been able to figure it out :/ Let V=4*L^3 cm^3, where dl/dt=10*t cm/s. Find dV/dt at t=0.1 second
  47. C

    Implicit 'higher' differentiation

    Hi, I'm working on a cal III problem involving implicit differentiation. I have to find the second order partial derivative of an implicit function, basically: \partial2f \partialx2 now, I know that for a single order \partialf/\partialx, I would simply use the chain rule property: \partialf =...
  48. S

    Find dy/dx by implicit differentiation: 6x^2+8xy+y^2=6

    Homework Statement Find dy/dx by implicit differentiation: 6x^2+8xy+y^2=6 Homework Equations n/a The Attempt at a Solution I'm using y'=(dy/dx) I found the derivative of the above problem. 12x+8xy'+10y=0 (I used the product rule to find the derivative of 8xy') 12x+8xy'+10y=0...
  49. R

    Logarithmic differentiation

    Question: Find derivative of f(x)=((x^2)(x^3))/((x^4)(x^2)) Attempt: ln f(x)=(lnx^2)+(lnx^3)-(lnx^4)-(lnx^2) Can someone tell me what I have done wrong so far? Thanks
  50. R

    How do I use implicit differentiation to solve these two questions?

    Im having trouble solving these two questions. I don't know where to start so I can't give an attempt at either of them. Please tell me how to do the full question if you can cause i can't check back until morning then i have to go to an exam. http://www.users.on.net/~rohanlal/one.jpg...
Back
Top