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. R

    Complex Differentiation sin(z) & cos(z)

    Hi There, I'm currently using the definition of exponential functions: e^z=(e^x)(e^iy) I need help defining: sin(z)=(e^(iz)-e(-iz))/(2i) cos(z)=(e^(iz)+e(-iz))/(2) And showing that sin'(z) = cos(z) cos'(z) = -sin(z) (sin(z))^2+(cos(z))^2=1 Any help would be appreciated...
  2. T

    Matrix determinants and differentiation

    I'm having trouble understanding where this concept comes from: Step 1) If you start out with the following two equations v + log u = xy u + log v = x - y. Step 2) And then perform implicit differentiation, taking v and u to be dependent upon both x and y: (d will represent the partial...
  3. E

    How do I find the derivative of f(x)=x+9/x without using the power rule?

    Homework Statement This is the larger problem to the small portion that I already posted in the Precalc Hw help forum. I still can't figure out how to get to the answer. The problem is this: I am trying to find the derivative of f(x)=x+\frac{9}{x}. Homework Equations I know via power...
  4. H

    Help: Implicit differentiation with initial values

    Homework Statement 2*y + sin(y) = x^4 + 4(x)^3 + (2(Pi) - 5), show that dy/dx = 16, when x = 1. Homework Equations The Attempt at a Solution So I implicitly differentiated it to be dy/dx(2 + cos(y)) = 4(x)^3 + 12(x)^2, and I end up with dy/dx = 16 / (2 + cos (y)) which means that...
  5. M

    Implicit Differentiation: Finding Derivatives of an Implicit Function

    Homework Statement Assume that the following equation define the implicit function y=(x). Find the its derivative: x2 + 2xy - y2 = a2 y'=? y''=? Homework Equations \frac{dy}{dx} = -\frac{F_x}{F_y} The Attempt at a Solution so for the first derivative I express that equation as...
  6. S

    Differentiation of damped motion function - Need help ly

    Differentiation of damped motion function - Need help urgently! Homework Statement Basically my task was to come up with a function to model the swing of a pendulum. The model I came up with was: 0.16e^{-0.25t}cos((\stackrel{2\pi}{1.22})t-0.8) + 0.814 The next part of my task asks me...
  7. K

    Implicit Differentiation and understanding the question?

    Hi, I am working on my differential equations excercises and I encountered 2 problems. First one is, I just wanted to check if I did this implicit differenriation right Homework Statement t^{2} \bullet y +y^{2} = C where is is a constant The Attempt at a Solution My solution is y...
  8. T

    Partial differentiation of a function

    Hi, I've got the following problem: Show that if z = x^nf(u) and u = y/x then x\frac{\partial{z}}{\partial{x}} + y\frac{\partial{z}}{\partial{y}} = nz I know partial differentiation fairly well, but I've never seen one laid out like this before, and am not too sure how to get started...
  9. B

    Differentiation of a function with respect to itself

    In one of my electronics textbooks I have the following equation related to feedback in amplifiers: K_f = \frac{K}{1-K\beta} \frac{dK_f}{K_f} = \frac{1}{1-K\beta}\frac{dK}{K} I'm not sure how this was derived - how was Kf differentiated with respect to itself?
  10. S

    Differentiation quotient rule question, am i wrong or is my book wrong?

    Differentiate with respect to x; (using the quotient rule) 3/2x-1 (3 over 2x minus 1) dy/dx = (2x-1)(0) - (3)(2) / (2x-1)^2 dy/dx = -6/(2x-1)^2 but my book gives -2/(2x-1)^2 now, y = u/v and i take u = 3 and v = 2x-1. dy/dx = v(du/dx) -...
  11. D

    Understanding differentials and differentiation

    I am very interested in math and I find calculus to be a particularly interesting subject, but one major problem I have with it is that I cannot find a consistent explanation of the rules of differentials (infantesimals) that explains all the things mathematicians do with them. I have truly...
  12. P

    Finding the Gradient of ln(tan2x+secx) Using Substitution | Homework Help

    Homework Statement By using cos and sin subs for tan and sec, find the gradient of: ln(tan2x+secx) Homework Equations tanx=sinx/cosx secx=1/cosx The Attempt at a Solution Substituting y=ln(\frac{sin2x}{cos2x}+\frac{1}{cosx}) Using the chain rule let: z=...
  13. N

    Where is the Function f(z) = (z+1)/(z-i) Differentiable on the Complex Plane?

    Homework Statement Find where; f(z) = (z+1)/(z-i) is differentiable on the complex plane and find the formulas for f' Homework Equations CR equations; if f(z) = u(x,y) + iv(x,y) u_x - v_y = 0 v_x + u_y = 0 if function is differentiable The Attempt at a Solution...
  14. J

    Differentiation problem and finding maximum, ing ?

    Differentiation problem and finding maximum, need helping :)? have a few problems with these questions, can you help :) Using differentiation, find the MAXIMUM value of the following functions? 1. f(x) = x2 / 4 + 4 / x 2. f(x) = xe-2x2 3. f(x) = sqrt(x - n) / x ; n>0 hope you guys...
  15. J

    Maximum values for differentiation

    maximum values for differentiation :( have a few problems with these questions, can you help :) using differentiation, find the maximum value of the following functions? 1. f(x) = -x2 + x 2. f(x) = lnx - x 3. f(x) = -x2 + 2x2 4. f(x) = x2/4 + 4/x 5. f(x) = xe-2x2 6. f(x) = sqrt(x -...
  16. J

    What are the best rules for solving differentiation problems?

    have a few problems with these questions, can you help :) 1. f(x) = -x2 + x 2. f(x) = lnx - x 3. f(x) = -x4 + 2x2 4. f(x) = x2/4 + 4/x 5. f(x) = xe-2x2 6. f(x) = sqrt(x - n)/x ; n>0 hope you guys can help !
  17. James889

    Simple differentiation problem, brainfart

    Hai, I have the easiest problem but I am stuck at the last step, simplification. \frac{cos3x+sin3x}{cos3x-sin3x} \begin{aligned} F(x) = cos(3x)+sin(3x)\\ F'(x) = -3sin(3x)+3cos(3x) \\ G(x) = cos(3x)-sin(3x) \\ G'(x) = -3sin(3x)-3cos(3x)\end{aligned} This gives...
  18. M

    Volume of a box using differentiation

    Hello :smile: I'm really stuck on a question and could do with some help. Homework Statement http://img268.imageshack.us/img268/2161/19947313.jpg Homework Equations http://img139.imageshack.us/img139/3478/24591171.jpg The Attempt at a Solution...
  19. G

    Is There a Complex Gradient Formula for Polar Coordinates?

    Does there exist anything like a polar complex differentiation? So there exists a gradient equation in polar coordinates something like \nabla{f} = \frac{\partial f}{\partial r} e_r + \frac{1}{r}\;\frac{\partial f}{\partial \theta} e_{\theta} But this is not for a complex number f(z) where...
  20. M

    Differentiation With 'x' Both in Base and in Exponent

    I have just begun studying differentiaition and I was getting confused with how to differentiate a function of x in which x is in the base and is in the exponent as well (for example, x^2x) with respect to a=hte cahnge in 'x'. I remember my teacher telling me something about applying log...
  21. K

    Laplace time differentiation property

    Hello, I'm trying to prove the time differentiation property of Laplace transform. dx(t)/dt = sX(s) http://img10.imageshack.us/img10/290/tlaplace.jpg http://g.imageshack.us/img10/tlaplace.jpg/1/ how do i continue from here ?
  22. M

    Explicit Equations for Implicit Set at (0,0): First Partial Derivatives

    Homework Statement Show that the set defined by the equations x + y + z + w = sin(xyzw) x - y + z + w^2 = cos(xyzw) - 1 can be described explicitly by equation of the form (z, w) = f(x, y) near the point (0,0,0,0); find the first partial derivatives of f(x,y) at the point (0,0)...
  23. T

    Differentiation by the Product Rule

    Hi I have been asked to solve the following 2 questions using 'rules' to find the derivative. (The Product Rule, The Chain Rule or The Quotient Rule.) but I can't remember what these rules are or how they are used Q1: Find the equation of the tangent to each of the following curves at the...
  24. Saladsamurai

    Partial Differentiation Help with Chain Rule

    In fluid mechanics velocity is given in the form \textbf{V}=u\textbf{i}+v\textbf{j}+w\textbf{k} Homework Statement A two-dimensional velocity field is given by \textbf{V}=(x^2-y^2+x)\textbf{i}+(-2xy-y)\textbf{j} At (x_o,y_o) compute the accelerations a_x\text{ and }a_y I am...
  25. Saladsamurai

    Partial Differentiation Troubles

    Homework Statement Okay, I know that I must be overlooking the obvious here, but here goes. Take some velocity function of time and space V(x,y,z,t) and we want to find its derivative, the acceleration vector a(x,y,z,t) If we have \vec{V}=u\hat{i}+v\hat{j}+w\hat{k} Then by chain rule...
  26. T

    Unforeseen Differentiation Problem in Chemical Concentration Equation

    I was working on some of my own equations and today i ended up with this differentiation thinghy, I never expected this in my equation but it just turned up :( so if there's anybody out there who loves to solve math please give this a try :) maybe its too simple :) ... i am just having doubts...
  27. K

    Laplace differentiation question

    Hi I'm learning laplace transform, specifically multiplying by 't' and 't^n'. Now i understand the concept that L{tf(t)} = -F'(s) but I'm confused with the differentiation part of the process (having a bit of a dim moment!). Here is the example it gives: L{sin2t} = 2 / (s^2 + 4), therefore...
  28. matt_crouch

    Differentiate with Respect to X

    Homework Statement Differentiate with respect to X Homework Equations 1) e^3x + ln2x 2) (5+x^2)^3/2 The Attempt at a Solution 1) isn't it just normal differentiation? so 3e^3x + 1/2x only thing i wasnt sure about was the differentiation of ln2x 2) second one i...
  29. P

    What Is the Correct Approach to Solve These Implicit Differentiation Problems?

    Homework Statement 8x^2-10xy+3y^2=26 2. The attempt at a solution (8)(2x)-(-10x)y'+(y)(-10)+(3)(2y)y'=0 16x+10x(y')-10y+6y(y')=0 y'(10x+6y)+16x-10y=0 y'(10x+6y)=10y-16x y'=(10y-16x)/(10x+6y) y'=(5y-8x)/(5x+3y) I know I'm doing something wrong but I can't see it for...
  30. S

    How can I differentiate ln(x) correctly?

    Homework Statement I am unsure how to differentiate ln(x). Homework Equations \int dx/ (x logex) The Attempt at a Solution I let u = logex So it became: \int x-1u-1dx To integrate I now need to find du/dx... which means differentiate ln(x). How does this work out?
  31. A

    Partial Differentiation [Subscript]

    What does the subscript outside a partial differentiation mean? For example: \left(\frac{\partial x}{\partial y}\right)_z What does the z mean above?
  32. O

    Can Differentiability of a Function be Extended to its Absolute Value?

    Homework Statement By the formal definition of differentiation Prove that if f differentiable in c and f(c)\neq0 then |f| differentiable in c. The Attempt at a Solution I know that if f differentiable do it also continues but I stuck because this fact correct necessarily only for...
  33. P

    What Went Wrong in This Differentiation Puzzle?

    This is just a pretty simple "riddle" that I have always liked a lot. I didn't come up with it, I actually got it off of a website a few years ago. I'm sure for some of you, it won't be new, but here goes.. x = x x = 1 + 1 + ... + 1 (x times) x(x) = x(1 + 1 + ... + 1) x2 = x + x + ... + x...
  34. S

    Least Square Minimisation and Partial Differentiation

    Homework Statement I am trying to understand how some equations are obtained in some lecture notes I have. This is my starting equation-http://i423.photobucket.com/albums/pp315/skaboy607/StartEquation.png And I need to satisfy these conditions...
  35. S

    How do I find f'(1) using implicit differentiation?

    "implicit differentiation" if [x][3] * f(x) + [(f(x))][3] + f([x][3]) = 3 and f(1)= 2 find f'(1) NEED HELP REVIEW QUESTION FROM EXAM REVIEW DONT KNOW WHAT TO DO
  36. W

    Can the differentiation variable be simplified to just one variable?

    I'm working out some problems, and I'm ending up with a term similar to the following: du/d(y/u) I'm differentiating with respect to y/u. Both y and u are variables. How can I divide that up to represent differentiation with just one variable (Even if it means expanding the term)? Is it...
  37. F

    Gradient of spherical co-ords/ differentiation help

    Homework Statement h(sph)=exp(r2sin2(\theta)sin2(\phi)+r2cos2(\theta)) need to find gradient of this function, i have er and etheta... but can someone please tel me why when maple differentiates with respect to phi, why does it say it equals zero? coz i get...
  38. M

    A run of the mill Implicit Differentiation

    Homework Statement Use Implicit Differentiation to find y' of the equation 5x^2+ 3xy+y^2=152. The attempt at a solution y'= (-10x-5y)/3x I would like to know if I did this right. I am not very confident in my math sometimes that why I came here. If i did this wrong will you please steer me...
  39. L

    Solve by Implicit Differentiation or Partial Differentiation?

    Homework Statement I've got a question more with the structure of how this problem is presented: If x^(sin y) = y^(cos x) Find \frac{dx}{dy}(\frac{pi}{4},\frac{pi}{4}) Homework Equations We have been taught to solve by implicit...
  40. L

    Application on Differentiation

    Homework Statement could someone please help me to answer the following problem: Suppose a wire 20 cm long is to be cut into two pieces. One piece is to be bent in the shape of an equatorial triangle and the other in the shape of a circle. How should the wire be cut so as to: a) maximize...
  41. T

    How Do You Analyze the Function g(x) = |f(x)| on the Interval (-3,3)?

    Homework Statement The function f(x) is defined as f(x)= -2(x+2)(x-1)^2 on the open interval (-3,3). a. Let g(x) be defined as g(x)= abs(f(x)) in the open interval (-3,3). determine the coordinate(s) of the relative maxima of g(x) in the open interval. Explain your reasoning. b. For...
  42. D

    Fourier Series (differentiation)

    Homework Statement sin(t)cos(nt) dt Homework Equations The Attempt at a Solution I tried setting u=sin(t) or cos(nt) or nt but none seems to work. Can someone give me a hint as what to set u equal to? Thanks.
  43. C

    Differentiation under the integral sign

    Homework Statement I am asked to compute d/dt of _{c}\int^{d} ( _{a}\int^{t} f(x,y)dx)dy for t \in (a,b) for a problem involving differentiation under the integral sign. [a,b] , [c,d] are in closed intervals in \Re f a continuous real valued function on [a,b] x [c,d] Homework...
  44. O

    Implicit Differentiation: Find Y

    Homework Statement Find y' Homework Equations The Attempt at a Solution My solution: it's correct?
  45. J

    Logarithmic Differentiation Help NeededA LOT OF PROCESS WORK IS SHOWN

    Use logarithmic differentiation to find: a.) d/dx of [(sin^-1(x^2)*sinh^-1(x^2))/(sin^4(x^2))] b.) d^2/dx^2 (sech^-1(e^(2*x))) work shown for a: let y= [(sin^-1(x^2)*sinh^-1(x^2))/(sin^4(x^2))] taking the natural logarithm of both sides: ln y= ln...
  46. J

    Logarithmic differentiation help needed work shown

    Use logarithmic differentiation to find: a.) d/dx of [(sin^-1(x^2)*sinh^-1(x^2))/(sin^4(x^2))] b.) d^2/dx^2 (sech^-1(e^(2*x))) work shown for a: let y= [(sin^-1(x^2)*sinh^-1(x^2))/(sin^4(x^2))] taking the natural logarithm of both sides: ln y= ln...
  47. P

    Implicit Differentiation - Tangent Line & Horizontal Tangents

    Homework Statement Find an equation of the tangent line to this curve at the point (1, -2). Homework Equations The Attempt at a Solution 2y' = 3x^2+6x y' = 3x^2+6x y'=3/2x^2+3x y+2=3(x-1) y+2=3x-3 y=3x-5
  48. P

    Implicit Differentiation with Sin

    Homework Statement Homework Equations The Attempt at a Solution
  49. S

    What is the Second Derivative Using Implicit Differentiation?

    Use Implicit Differentiation to find y" if xy + y - x = 1 so far i got 1y + dy/dx - dx/dx = 1/dx then i did y + y' - 1 = 0 y' = 1-y i don't understand how to get the y" . i don't think i even have y' done right!
  50. C

    Applications of Differentiation II

    Homework Statement A research studied the commercial fishing situation in a certain fishing zone. Denoting the total catch of corel fish in that zone in t years time from January 1, 1992 by N(t) (in thousand tonnes), he obtained the following data: t=2, N(t)=55 t=4, N(t)=98 The...
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