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

    Implicit Differentiation: Solving for dy/dx in (x^2-y^2)^2=(x+y)^3

    (x^2-y^2)^2=(x+y)^3 I tried to use the chain rule on both sides but it didn't work because y needs to have the chain rule used on it explicitly and if i differentiate y explicitly then use the chain rule on everything i would be finding the 2nd derivative. So how do i differentiate this?
  2. T

    Parametric Equation Differentiation

    Homework Statement A curve has parametric equaions: x = 2cot t, y = 2sin²t, 0 < t <= pi/2 Find an expression for dy/dx in terms of the parameter t The Attempt at a Solution Not sure where to go. Do i need to make a Cartesian equation first? Thanks :)
  3. O

    Differentiation of displacement and time to get velocity

    [SOLVED] Differentiation of displacement and time to get velocity A moving body is related to a fixed point by the displacement equation: s = 12( 1 - e^-t). Assuming the body is moving in a straight line on a flat plain. 1. obtain an expression for the velocity after time t seconds. 2...
  4. H

    What is the formula for velocity in SHM using differentiation?

    Hey there, this should be a very simple problem, but again, I haven't had much guidance in finding formulas with differentiation. If anyone could help me with this i'd greatly appreciate it as it can help me to understand the others. Characteristics of SHM are displacement (x) and time (t)...
  5. T

    Tricky Trig Differentiation: Solving for dy in Terms of x | Homework Help

    Homework Statement x = 5sin(2y +6) find dy in terms of x Homework Equations The Attempt at a Solution dx/dy = 8 cos (2y+6) dy/dx = 1 / (8cos(2y+6) but according to the mark scheme the final answer is + or - 1 / (2 sqrt[16/x^2]) i don't see how on Earth they got...
  6. R

    Differentiating U_{ave} with respect to beta using summation notation

    Homework Statement Find \frac{dU_{ave}}{d\beta} where U_{ave}=\sum_{k}\left(\frac{U_{k}exp(-U_{k}\beta)}{exp(-U_{k}\beta)}\right) Homework Equations The Attempt at a Solution My answer is supposed to be -(U_{ave}^{2})+(U_{ave})^{2} However I keep getting zero. I can...
  7. F

    Implicit differentiation to find the slope

    Homework Statement (x - h)^2 + (y - k)^2 = r^2 where h,k and r are constants The Attempt at a Solution \begin{array}{l} \frac{d}{{dx}}\left[ {(x - h)^2 + (y - k)^2 } \right] = \frac{d}{{dx}}r^2 \\ 2(x - h) + 2\frac{{dy}}{{dx}}(y - k) = 0 \\ \Rightarrow \frac{{dy}}{{dx}}...
  8. K

    Simple partial differentiation

    Homework Statement Differentiate f = arctan(u/v) with respect to u The Attempt at a Solution Using the chain rule fu = (1/(1 + (u/v)2)) * 1/v = 1/(v + u2/v) The solutions manual says v/(u2 + v2) What is my mistake?
  9. G

    Proof of f''(a): Continuous Differentiation at a

    Homework Statement Prove that if f''(x) exists and is continuous in some neighborhood of a, than we can write f''(a)= \lim_{\substack{h\rightarrow 0}}\frac{f(a+h)- 2f(a)+f(a-h)}{h^2} The Attempt at a Solution I just proved in the first part of the question, not posted, that...
  10. G

    Real Analysis, differentiation

    Solved: Real Analysis, differentiation Homework Statement If g is differentiable and g(x+y)=g(x)(g(y) find g(0) and show g'(x)=g'(0)g(x) The Attempt at a Solution I solved g(0)=1 and I got as far as g'(x)=\lim_{\substack{x\rightarrow 0}}g(x) \frac{g(h)-1}{h} but now I...
  11. M

    Implicit differentiation dy/dx=xy^2

    Homework Statement If dy/dx=xy^2 and x=1 when y=1, then y= (A) x^2 (B) -2/(x^2 -3) (C) x^2 + 3 (D) 2/(x^2 +1) (E) (x^2 -3)/2 Homework Equations The Attempt at a Solution dy/dx=xy^2 dy=xy^2dx dy/y^2=x dx ∫dy/y^2=∫x dx -1/y = x^2/2 + C y=-2/x^2 + C 1=-2/1^2 + C C=3...
  12. D

    Simple differentiation question

    helicopter moves vertically. Height above start point = y height at t seconds = y= (1/4)t^4 -26t^2 + 96t t = between 0 and 4 differentiate to find velocity = t^3 + 52t + 96 acceleration = 3t^2-52 thats part 1 of question done, easy.Verify that y has a stationary value when t =...
  13. B

    How to Evaluate the Derivative of a Logarithmic Function with a Base of 10?

    Homework Statement if g(t)=(10^t)(log...t) then evaluate g'(10) ......10 <---------(my attempt at a log base 10) Homework Equations im completely lost...i don't know if i should take the ln of both sides...or what to do really. The Attempt at a Solution
  14. M

    How do I differentiate this equation for a test tomorrow?

    I need help differentiating this equation: y=(x-1)^2(6^x) What I have (I went wrong somewhere): dy/dx = (x-1)[(x-1)(6^x)] =(x-1)[6^x(1+ x ln6 - ln6) =(x-1)6^x(1+ x ln6 - ln6) So; My final answer: (x-1)6^x(1+ x ln6 - ln6) Answer in the textbook...
  15. 1

    Differentiation - Help, Please!

    Differentiation ---Help, please! 1. Homework Statement 1) Use Newtons Method to approximate the real zero of the function f(x)=x^3 + 7x + 3 = 0 2) The curve y = x^3-2x^2+x-3 intersects the curve y = cos(2x). If x = 1.8 is used as the first estimate then, using Newton's Method, what is the...
  16. U

    Implicit differentiation? implicit integration?

    We have implicit differentiation: i.e. x^2 + y^2 = 7 -> 2x +2y(dy/dx) = 0. and solve for dy/dx gives you the derivative of y with respect to x However, is there not implicit integration? for terms linear in y, i.e. x^2 + y = 7 -> X^3/3 +int(y) = 7x + K, and solve for int(y) to...
  17. T

    Differentiation of Geomertic Objects

    [URGENT] Differentiation of Geomertic Objects Homework Statement A sector of a circle has area 100cm². Show that the perimeter of this sector is given by te formula P = 2r + 200/r Homework Equations Area of sector = (angle/360) x pi x r^2 Permiter of sector = (angle/360) x 2 pi x r...
  18. D

    Differentiation Help: Answers & Explanations

    Help please on these. I'm extremely rusty with differentiation and want to know if I've got the right answers here Homework Statement differentiate the following functions (you do not have to simplify): a. f(x)=(x-2)^{3}e^{-2x} b. f(x) = cos x / ln (x^{2} + x) c. g(t) = cos^{4}(t^{2} +...
  19. B

    Implicit Differentiation of Cylinder NOT given radius?

    Implicit Differentiation of Cylinder NOT given radius? Homework Statement Question: Digging in his backyard, Dennis accidentally breaks a pipe attached to his water sprinkling system. water bubbles up at a rate of 1 cm^3/s, forming a circular pond of depth 0.5cm in his yard. How quickly is...
  20. B

    Understanding the Chain Rule in Vector Potential Derivations

    we are given some component of a vector potential A A = B\displaystyle\int^d_0 I(t')\,dt' where d = t -z/c and B = constant=1/2 mu0 (permeability constant) x c (speed of light) the derivation then wants me to calculate the magnetic field from this vector potential...
  21. Hootenanny

    Term-wise Differentiation of Power Series

    For those who don't know I'm writing a tutorial (https://www.physicsforums.com/showthread.php?t=139690") in the tutorials forum. I have come to the point of introducing Transcendental functions. I would like to introduce the exponential function first (via the Taylor series) and then present...
  22. S

    Implicit differentiation and chain rule-

    The question and my workings are attached:
  23. M

    What is fx(0,1) in Partial Differentiation for f(x,y)=2e^(x^2y)?

    f(x,y)=2e^(x^2y), then fx(0,1) = ? fx = 4xye^(x^2y) =4(0)(1)e^(0)(1) =e^0 =1? I'm told that I'm getting this question wrong but don't know how. Can anybody please help show me what I'm doing wrong on this one?
  24. Z

    Differentiation of potential energy

    Homework Statement The potential energy of a system of two particles separated by a distance r is given by U(r) = (A)/(r^4), where A is a constant. Find the radial force that each particle exerts on the other. (Use A and r as appropriate in your equation.) Homework Equations F=-dU/dx U is...
  25. 1

    Calculus Homework Help: Differentiating Trigonometric and Polynomial Functions

    Homework Statement 1) If f(x)= sin^4x, then f '(pi/3) 2) Given f(x) = x/tanx, find f '(3pi/4) 3) If f(x) = sinxcosx, then f '(pi/6) 4) Differentiate: f(x) = x^2 + 2tanx Question that I have answered but not sure if it's really the right answer: 5) Find the equation of the tangent line...
  26. C

    Another differentiation question

    Homework Statement Supposed "f" is a differentiable function. Write the expression for the derivative of the following function. a) h(x) = -4x^3 * f(x) b) h(x) = 2/\sqrt{x}* f(x) Homework Equations N/a The Attempt at a Solution Would the answers just be (using the product...
  27. C

    How Do You Find Absolute Extrema of a Polynomial Function?

    simple SIMPLE local extremia question Homework Statement Find the absolute maximum and absolute minimum values of f(x) = 3x^4 - 8x ^3 + 12x^2 -48x +25, where 0 <= x <= 3. Homework Equations N/a The Attempt at a Solution f'(x) = 12x^3 - 24x^2 + 24x -48 = 12 (x^3 - 2x^2 +...
  28. D

    Calculating a deriv using logarithmic differentiation

    Hello,This is my first crack at using log differentiation, but I can't seem to get too far with it... Use logarithmic differentiation to calculate the derivative for the following function: y = \sqrt{x}e^{x^{2}} (x^{2} + 1)^{10} lny = \frac{1}{2}lnx * x^{2}lne * 10ln(x^{2} + 1)...
  29. H

    Implicit Differentiation [SOLVED]

    [SOLVED] Implicit Differentiation -4x^2+3xy+4y^3=-328 This is at the point (3,-4) and i am trying to find m Homework Equations The Attempt at a Solution here is my work -4x^2+3xy+4y^3=-328 -8x+3xy'+3y+12y^2y'=0 -8x+3y=-3xy'-12y^2y' -8x+3y=[-3x-12y^2]y'...
  30. H

    What is the error in this implicit differentiation problem at the point (1,3)?

    [SOLVED] Implicit Differentiation [b]-4x^2+3xy+4y^3=-328 This is at the point (1,3) Homework Equations The Attempt at a Solution here is my work -4x^2+3xy+4y^3=-328 -8x+3xy'+3y+12y^2y'=0 -8x+3y=-3xy'-12y^2y' -8x+3y=[-3x-12y^2]y' y'=(-8x+3y)/(-3x-12y^2) plug in x=1,y=3...
  31. F

    What does this notation mean in terms of differentiation?

    http://img442.imageshack.us/img442/6018/scoreqt9.jpg Can someone explain what this notation means regarding differentiating please. I've never seen it this way using the integration symbol, so I have no idea where to start. :) thx
  32. O

    Implicit differentiation question

    Find y' = dy/dx for x3 + y3 = 4 Okay, now what's really confusing me is that for the y3 is that you need to use the chain rule for it. When you do, the answer is 3y2(dy/dx). How does that actually work? And if anyone can give me any good advice on any good guidelines on how to properly...
  33. 7

    Differentiation of cos(x)cos(y) or sin(x)sin(y)

    [SOLVED] differentiation of cos(x)cos(y) or sin(x)sin(y) Homework Statement Determine if the equation is exact, if exact solve. [cos(x)cos(y)+2x]dx-[sin(x)sin(y)+2y]=0 Homework Equations I have forgotten how to take the derivative of cos(x)cos(y) or sin(x)sin(y). Is this a product rule...
  34. G

    How Do You Differentiate f(x,y) = e^(2x) * ln(x/y^2) with Respect to x?

    f(x,y)=e2x*ln(x/y^2) find f(subscript-x) Can anyone help me with this differentiation please? I know you must treat y as a constant and differentiate with respect to x.
  35. J

    Technical question in multi-variable differentiation

    Let f(x+iy)=u(x,y)+iv(x,y). Suppose we know |f|^2=u^2+v^2 is a constant function. Then we are allowed to say that (u^2+v^2)_x=(u^2+v^2)_y=0. But are we allowed to differentiate u by x and v by y? IE, are we allowed to make the following statement: (u^2)_x+(v^2)_y=0 I'm guessing 'no', but...
  36. L

    What is the stationary point and its nature for the function f(x) = x^2-8x+4?

    Question: For the graph x^2-8x+4 : (i) find the coordinates of the stationary point; (ii) say, with reasoning, weather this is a maximum or minimum point; (iii) check your answer by using the method of 'completing the square' to find the vertex; (iv) state the range of values which the...
  37. B

    How to Solve Implicit Differentiation Problems with Tan(xy)=xy?

    okay, so i have the problem tan(xy)=xy and i am told to implicitly differentiate in terms of x and y. when i do, i keep getting an indefinite answer. i need help because i know that's not right.
  38. S

    When is a function bounded using differentiation

    Homework Statement how do i determine whether a function is bounded using differentiation eg: f(x)=x/(2^x) Homework Equations The Attempt at a Solution i know it has something to do with maximums and minimums but i can't figure out how to do it. any help would be appreciated...
  39. B

    Implicit differentiation of one-parameter family

    Homework Statement Use implicit differentiation to show that the one parameter family f(x, y)=c satisfies the differential equation dy/dx = -f_{x}/f_{y} , where f_{x}=\frac{\partial f}{\partial x} and f_{y}=\frac{\partial f}{\partial y} .Homework EquationsThe Attempt at a Solution Well, my...
  40. E

    Help on differentiation of tensor fields

    Given a tensor field T(x,y,z), how would I go about differentiating it wrt spatial coordinates? I would presume that it would work like this: \begin{equation} \frac{\partial T}{\partial x} = \lim_{h\to 0}\frac{T(x+h,y,z)-T(x,y,z)}{h} \end{equation} However, this does not seem to...
  41. D

    Why is the Coordinate of Point P (3/2, 0) in this Differentiation Problem?

    "the equation of a curve is x^2y=x-6 (x^2y is x squared times y) The normal of the curve at the point where x=-2 meets the x-axis at p. Find the coordinates of P" The method I used was to find y by rearranging the given equation and differentiate it. This gave me f ' (x)= 1+12x^-3...
  42. A

    How Do You Solve Second Derivatives Using Implicit Differentiation?

    Hi, I need some help with these question, and would appreciate the help. Homework Statement Part 1 Use implicit differentiation to find y'' if 2xy = y^2 Simplify and Leaev in terms of x and y. Part 2 Use implicit differentiation to find y '' if xy + y^3 = 1 Simplify your answer and...
  43. Gib Z

    Differentiation operators similar to exponents?

    I was just messing around on another problem I was trying to solve for someone in the homework forums when I stumbled on this: If we denote the n-th derivative the same way we do for exponents, eg the second derivative of f will be denoted by f^2, and the original function as its zero-th...
  44. Cyrus

    The contiunity equation and differentiation

    The contiunity equation is given as: ln(\rho) + ln(A) + ln(V)=constant "Differentiating Eq. 11.43 we get: \frac{d\rho}{\rho}+ \frac{dA}{A} +\frac{dV}{V}=0 My question is, what is this differentiated with resepct to? Its clearly not \rho, A or V alone.
  45. P

    Trig Differentiation Memorization help

    Hey guys, I'm having trouble memorizing the the derivatives of the trig functions. I can memorize them for a while, but I eventually forget them all after one day. Does anyone know any sort of hooks or tricks that will make this process easier?
  46. D

    What is the Derivative of Functions with Radical and Fractional Exponents?

    I'm having trouble with the following questions about differention with respect to x. Differentiate with respect to x: a) y= 2/ (2x+3)^4 b) y= x(x+1)^(1/2) c) y= (x +1)(x^2 + 3x)^3 d) y= 3x^3 + 3x^(-1/2) + 2 Any help would be greatful
  47. U

    How do I solve for partial differentiation in multivariable calculus?

    Ok here goes... z=x^{2}+y^{2} x=rcos\vartheta y=r sin\vartheta Find: \[ \frac{\partial z}{\partial x}_{y}, \[ \frac{\partial z}{\partial \vartheta}_{x}, \[ \frac{\partial z}{\partial r}_{y}, \[ \frac{\partial z}{\partial r}_{ \vartheta}...
  48. N

    Linear algebra - differentiation operator

    Homework Statement I have a differentiation operator on P_3, and: S = {p \in P_3 | p(0) = 0}. I have to show that 1) D maps P_3 onto the subspace P_2 2) D : P_3 -> P_2 is NOT one-to-one 3) D: S -> P_3 is one-to-one 4) D: S -> P_3 is NOT onto. The Attempt at a Solution...
  49. J

    Can the car stop in time at the stop sign?

    Homework Statement A car, traveling at a speed of 90km/h, approaches a stop sign 40m ahead. If the car immediately begins to decelerate at a rate of -8m/s^2, will it be able to stop in time? Justify your response Homework Equations d = 1/2at^2 + vt The Attempt at a Solution I...
  50. J

    Differentiation maximum problem

    Power of an electrical circuit is equal to current squared times resistance. My expression for current is: E/(R + r), where E is emf of battery. So, my expression for Power, P, is: P=((E^2)R)/(R + r)^2 I would like to differentiate P with respect to R, to find where the slope is...
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