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. E

    What is the value of vector a at t=pi given the initial conditions?

    Homework Statement The vector a depends on a parameter t, i.e. a=a(t)=a_x(t)i +a_y(t)j +a_z(t)k.. it satisfies the equation da/dt= j \times a show that d^2a_x/dt^2 =-a_x , da_y/dt=0 and d^2a_z/dt^2 =-a_z. For the vector a, find its value for t=pi if at t=0 a(0)=i+j and da/dt(0)=0k...
  2. Chewy0087

    Simple Partial Differentiation

    Homework Statement Hey >.< another simple problem; find \frac{\partial u}{\partial y} , \frac{\partial v}{\partial y}, \frac{\partial w}{\partial y} given that u - v + 2w = x + 2z 2u + v - 2w = 2x - 2z u - v + w = z - y The Attempt at a Solution I don't know, this question is really...
  3. Z

    Differentiation - Quotient rule

    Homework Statement Given y = x^2 + 6 / x find x if dy/dx equals 0 zero Homework Equations dy/dx = v du/dx - u dv/dx / v^2 The Attempt at a Solution I have got as far as dy/dx = x^2 - 6 / x^2 However then zero must equal Sqrt 6, which 2.44... -...
  4. R

    Partial Differentiation Confusion

    Homework Statement Find \frac{\partial z}{\partial x} \frac{\partial z}{\partial y} where z=\left( [x+y]^3-4y^2 \right)^{\frac{1}{2}}Homework Equations -The Attempt at a Solution I know that \frac{\partial z}{\partial y}=\frac{3(x+y)^2-8y}{2\sqrt{(x+y)^3-4y^2}} but I am unsure whether...
  5. L

    Implicit differentiation

    Homework Statement find \frac{\mathrm{d}y}{\mathrm{d}x} where y is defined implicitly as a function of x Homework Equations x\sin(xy)=x The Attempt at a Solution x(\cos(xy)(x\frac{\mathrm{d}y}{\mathrm{d}x}+y))+\sin(xy)=1...
  6. H

    Question involving differentiation

    Homework Statement Prove that if F is a twice differentiable function with F(0) = 0 and F(1) = 1 and F'(0) = F'(1) = 0, then |F''(x)| >= 4 for x in (0,1). Hint: Prove that either F"(x) >= 4 for some x in (0,1/2) or else F"(x) <= -4 for some x in (1/2,1) Then, show that we...
  7. B

    Trigonometry differentiation problem

    Homework Statement Differentiate the following cos^2 x The Attempt at a Solution \frac{d(cos^2 x)}{dx} = 2 (-sin^{2-1} x).\frac{dx}{dx} = 2 (-sin x).1 = -2 sin x But the answer given is- -2 cos x sin x Can you please tell me what's wrong !
  8. S

    Differentiating a Sum in MATLAB

    Homework Statement How do i differentiate a sum in MATLAB? So for an example, if I have: y = x^2 + \sum^{n}_{j=1}3x_{j}^4 I want to differentiate it with respect to x. It should return: 2x + \sum^{n}_{j=1}12x_{j}^3 Homework Equations The Attempt at a Solution If I want...
  9. P

    How Do You Tackle Partial Differentiation with Trigonometric Functions?

    Homework Statement If x = yz and y = 2sin(y+z), find dx/dy and d^2x/dy^2 Homework Equations The Attempt at a Solution I am beyond confused at how to even start this one, the problem is not like any of the examples in my book. I know x = ydz + zdy but don't know how to deal...
  10. Q

    Vector differentiation of velocity (polar coord.)

    The velocity of a particle moving in a plane in polar coordinates is {\bf{v}} = v_r {\bf{\hat r}} + r\omega \hat \theta where v_r = \frac{{dr}}{{dt}} and \omega = \frac{{d\theta }}{{dt}}. By differentiating w.r.t. time, show that the acceleration of the particle is {\bf{a}} =...
  11. L

    How can I solve the partial differentiation equation provided?

    Homework Statement http://img94.imageshack.us/img94/3853/physicse.jpg The Attempt at a Solution I kept y fixed, and so I ended up with the following equation: Integ[dU/U] = Integ[x] And we end up with: U(x,y) = e^x * g(y) To solve g(y), we sub the solution into the 2nd PDE provided to...
  12. S

    Differentiation practicing materials?

    Hello, I`m studying 1st year physics and I would really like to improve my basic maths. The thing is I don`t want to sit and first make up a random expression and then calculate the derivative, I would like to be able to print out hundreds and hundreds of small expressions with varying...
  13. J

    Proof using implicit differentiation

    Prove that if P(a,b) is a point on the rotated ellipse C (whose equation is x^2 -xy +y^2=4 ), then so is Q(-a,-b), and that the tangent lines to C at P and Q are parallel. The equation of the line joining P and Q is y - b = m(x - a), where m= \frac{b-(-b)}{a-(-a)} = \frac{b}{a}, then the...
  14. Salazar

    Swimming Pools and Related Rates along with Implicit Differentiation

    Homework Statement A swimming pool is 40 feet long, 20 feet wide, 4 feet deep at the shallow end, and 9 feet deep at the deep end. Water is being pumped into the pool at 10 cubic feet per minute. a. When the water is 3 feet deep at the shallow end, at what rate is the water level rising? b...
  15. A

    Partial Differentiation: How Do You Differentiate Arc Tangent Terms?

    I was working through this problem, I understand the method, but got stuck trying to differentiate the arc tan terms... In the table of standard derivatives, \frac{d}{dx} \arctan{x} = \frac{1}{1+x^2} and for PDE's, you treat y as constant when differentiating w.r.t. x --- Any...
  16. Salazar

    Air Traffic Controller and Related Rates along with Implicit Differentiation

    Homework Statement "An air traffic controller spots two planes at the same altitude converging on a point as they fly at right angles to each other. One plane is 120 miles from the point and is moving at 400 miles per hour. The other plane is 160 miles from the point and has a speed of...
  17. M

    Simplifying the Derivative of a Complex Rational Function

    find derivative of y=(sqrt(8x^4-5))/ (x-1) ok...after working out the tricky calculations i get for my final answer: (32x^4sqrt(8x^4-5)-64x^3sqrt(8x^4-5)) / (16x^6-32x^5+ 16x^4-10x^2+20x-10) I don't know if you want to do the math...im just wondering if i can simplify it anymore. thanks
  18. S

    Simple differentiation question

    A Norman window has the shape of a square surmounted by a semicircle. The base of the window is measured as having 80cm with a possible error in measurement of 0.1cm. Use differentials to estimate the maximum possible error in computing the area of the window. So what i did was...
  19. S

    Deriving the Heat Equation with Exponential Term: Can We Solve for exp(theta)?

    Homework Statement I'm having trouble deriving the following equation \frac {\partial^2 {\theta}}{\partial {x'^2}} = -y^2*exp(\theta) and y = x/x' my main problem is the exponent Homework Equations The Attempt at a Solution Normally i would use the equation (x')'' + k^2*x' = 0 x' = c1...
  20. M

    Differentiation using a constant question

    Homework Statement If f'x = 0 \forall x \in (a,b), show that f is constant there. I've gotten a final result, but I'm not entirely sure if I actually showed what I intended to show... Homework Equations The Attempt at a Solution Fix a point c \in (a,b) and choose a point x...
  21. Sirsh

    Finding Values for a and b: Tangent and Perpendicularity in y=ax^3 and y=2x+3

    The tangent to the curve y=ax^3 at the point (-1,b) is perpendicular to the line y = 2x+3. Find the values of a and b. Could someone show me how to answer that?
  22. S

    Need help with a Differentiation Question

    Homework Statement Differentiate f(x) if f(x)=xxln(3x-6) Homework Equations None The Attempt at a Solution The problem in f(x) is the xx so what I did was let a=xx and differentiated a with respect to x. I ended up with da/dx= (ln(x)+1)xx. Afterwards, I modified f(x) by...
  23. B

    Change of variable, second order differentiation

    Okay, so my problem lies within taking the second derivative of a change of variable equation. w = f(x,y); x = u + v, y = u - v so far I have the first derivative: dw/dx = (dw/dv)(dv/dx) + (dw/du)(du/dx) = (d/dv + d/du)w Now I'm having problems in finding my second derivative...
  24. T

    Finding Points on a Curve with Tangent Line Slope -1

    Homework Statement Find all the points on the curve x^{2}y^{2}+xy=2 where the slope of the tangent line is -1. The Attempt at a Solution I differentiated both sides of the equation and got: \frac{dy}{dx}=\frac{-2xy^{2}-y}{x^{2}2y+x} I know that \frac{dy}{dx}=-1, but if I substitute...
  25. matt_crouch

    How do I differentiate m(L^2)/16?

    Homework Statement i have been told to calculate DI/Dx i calculated I as being = m(L^2)/16 how do i differentiate this? I am confussed with what happens to the m is it a constant an just removed? same with the 1/16 i assume that is removed as a constant? just need some clarification...
  26. L

    Implicit Differentiation w/ Composite Function

    Homework Statement Given the equation y= f(x) , at a certain point the slope of the curve is 1/2 and the x-coordinate decreases at 3 units/s. At that point, how fast is the y-coordinate of the object changing? The Attempt at a Solution Dy/dx = f ' (x) dx/dt Would that be...
  27. R

    Differentiation, Product Rule 3-terms

    Homework Statement f(x) = (2x-1)(3x-2)(5x+1) d/dx = ? Note that I am letting (2x-1)(3x-2) = f and 5x+1 = g Homework Equations d/dx (fg) = f d/dx g + g d/dx f The Attempt at a Solution d/dx y = (2x-1)(3x-2)d/dx(5x+1)+(5x+1)d/dx((2x-1)(3x-2)) = (2x-1)(3x-2)(5)+...
  28. R

    How do I differentiate (x^(3)+2x) / (x^(2)-5)?

    Homework Statement (x^(3)+2x) / (x^(2)-5) d/dx = ? Homework Equations d/dx (f/g) = (g d/dx (f) - f d/dx (g)) / g^2 The Attempt at a Solution d/dx y = { (x^(2)-5) d/dx (x^(3)+2x) - (x^(3)+2x) d/dx (x^(2)-5) } / (x^(2)-5)^2 This is where it gets complicated for me. {...
  29. I

    Differentiation - slopes

    Homework Statement Find the slope of the curve y=\frac{x}{3x+2} at the point x = -2. Homework Equations \lim_{h \rightarrow 0}\frac{f(x_{0} + h) - f(x_{0})}{h} = m The Attempt at a Solution If x = -2, then y = 1/2. I'm not sure what to do from here. This is the first step, but I don't get...
  30. J

    Implicit Differentiation: Finding Tangent Line and Second Derivative

    Homework Statement Consider: x^3+y^3+2xy=4, y=1 when x=1 a.) Find the equation of the tangent line to the curve when x=1. b.) Find y'' at x=1. c.) Is the graph of y=f(x) concave up or concave down near x=1? Homework Equations Any derivative rules... The Attempt at a Solution For Part a...
  31. C

    Differentiation of exponential

    Homework Statement y = x^(18x^-4) Homework Equations chain rule dy/dx a^x = a^x ln a The Attempt at a Solution first i used the second equation from above to get x^(18/x^4)*ln(x) then i use the chain rule to get x^(18/x^4)*ln(x)*(-72x^-5) the computer program i am using is...
  32. Q

    Deriving Inverse Trig Functions: A Step-by-Step Guide

    Alright, I'm not technically stuck on this one, but I consistently get a result that disagrees with what Wolfram Alpha shows when I enter the problem to check my answer. Sorry 'bout the lack of LaTeX, but it should be simple enough to read. Here goes: Problem: Differentiate y=sin-1[x/(1+x)]...
  33. L

    Differentiation, Second Derivative, of Functions Problem

    Homework Statement Suppose f(3)=2 , f'(3)=5 , and f''(3)= -2 . Then d²/dx² (f²(x)) at x=3 is equal to ____? A. -20 B. 20 C. 38 D. 42 E. 10 The Attempt at a Solution I am confused about how to find the function to get the derivative from that function. Any Ideas? Thanks.
  34. D

    Understanding Implicit Differentiation: Solving for Second Order Derivatives

    Find d^2/dx^2(3y^2+8y=3x) I managed to get dy/dx = 3 / (6y + 8) but I have no clue where to go from here. According to WolfRamAlpha, the answer is -27/(4(16 + 9x)(4 + 3y)), but since dy/dx doesn't have any x value in it, I don't see how the derivative of it would. I've played around...
  35. D

    Implicit differentiation problem.

    Homework Statement Find y´(x) for x + y = 1/x^2 + 8/y^2 Homework Equations The Attempt at a Solution Rewrite the eq. as x + y = x^-2 + 8y^-2 differentiate. 1 + y´(x) = (-2x^-3) + (-16y^-3)(y´(x)) Rearrange 1 + (2x^-3) = (-16y^-3)(y´(x)) - (y´(x)) (1 + (2x^-3))/(16y^-3) =...
  36. S

    Differentiation Rules - Products~

    1. Suppose the curve f(x)=(x^4)+a(x^3)+b(x^2)+cx+d has tangent line when x=0 with equation y=2x+1, and a tangent line when x=1 with equation y=2-3x. Find a,b,c,d 2. d/dx f(x)g(x)=g*f`+f*g` 3. f`(x)=4x^3+3ax^2+2bx+c x=0 y=2x+1 y=1 (0,1) is a point on f(x) x=1 y=2x-3 y=-1 (1,-1) is a point on...
  37. C

    What is the Derivative of g(x) when x=0 in the Equation g(x) + x sin g(x) = x^2?

    Homework Statement If g(x) + x sin g(x) = x^2 find g'(0) Homework Equations The Attempt at a Solution At this point I have tried a few things but hit deadends. Any help would be appreciated.
  38. Chewy0087

    Integration by Parametric Differentiation

    Homework Statement Having trouble understanding this the example I saw was; Solve \int^{\infty}_{0} x^3 e^{-9x} dx using integration by parametric differentiation.The Attempt at a Solution well, i do know how to do this, so i set out my integral; \int^{\infty}_{0} e^{-\alpha x} dx =...
  39. B

    Find y'' by implicit differentiation

    Homework Statement Find y'' by implicit differentiation. Homework Equations The Attempt at a Solution I get to this point in the problem, which is I solved for y'. But then when I attempt to take y'', in other words take the derivative of my answer for y', I...
  40. M

    Implicit differentiation find dy/dx and d2y/dx2

    2xy=3x-y^2 find dy/dx and d2y/dx2 I just want to make sure my answer is right and simplified I got dy/dx= (3-2y)/ (2x+2y) Now d2y/dx2 took some time but this is what i got: (-12x+2x2y+9+4yx-14y-4y^2) / ((x+y)(2x+2y)^2)
  41. T

    Order of differentiation and integration

    I guess the following identity isn't right. Can anyone tell me what the LHS is really equal to? \frac{\partial}{\partial x}\int_{-\infty}^\infty\int_0^x f(s,t) dsdt = \int_{-\infty}^\infty f(x,t)dt
  42. T

    Implicit differentiation on x^3 + y^3 = 4xy + 1

    1. use implicit differentiation to evaluate y(prime) for x^3+y^3=4xy+1 at the point (2,1)
  43. A

    Solve using implicit differentiation 6 y+8 x=\sin(xy^2)

    so to solve this i differentiated each part and got 6dy/dx + 8 = cos(xy^2)(y^2*x2ydy/dx) then i divided both sides by cos(xy^2) then serpatated the 6dy/dx + 8 and put them both over cos(xy^2) then i took out a yprime and ended up with -8/(6-2y^3xcos(xy^2)) as an answer but its wrong...
  44. J

    Differentiation Ax^b with f(x) already given

    Homework Statement The function f is defined as f(x)=x^4, then; f'(3x^3)=? d[f(3x^3)]/dx=? f'(xy^3)=? Homework Equations The Attempt at a Solution My problem here is not so much doing the differentiation itself but understanding the notation. 1. for f'(3x^3) i want...
  45. M

    Some help with this differentiation question thanks

    some help with this differentiation question thanks Question : Find the indicated partial derivative . frss , frst f(r,s,t) = r ln (rs^2t^3) differentiating with respect to r gave s^2t^3 1* ---------- rs^2 t^3 but this is not correct something is...
  46. V

    Doubt about Implicit differentiation

    Hi all, I was reading a paper in which implicit differentiation was used as follows x \in R, \lambda \in R Given G(x,\lambda) = 0 \frac{\partial G(x,\lambda)}{\partial x} \frac{\partial x}{\partial \lambda} + \frac{\partial G(x,\lambda)}{\partial \lambda} = 0 My doubt is...
  47. L

    Implicit Differentiation and product rule

    Hi, So, I am reviewing Cal III, and I have come across something that I do not understand regarding implicit differentiation with partial derivatives: x^3 + y^3 + z^3 + 6xyz = 1 implicit differentiation of z with respect to x: 3x^2 + 3z^2(dz/dx) + 6yz + 6xy(dz/dx) = 0 *notive the...
  48. D

    How can the derivative of a differentiable function be expressed using limits?

    Homework Statement Prove if f(x) is differentiable at x=a then f'(a)=lim_{h\rightarrow0}\frac{f(a+h)-f(a-h)}{2h}Homework Equations I know that the derivative is defined as f'(a)=lim_{x\rightarrow a}\frac{f(x)-f(a)}{x-a}The Attempt at a Solution Starting from the definition I used a known...
  49. G

    Proving g is a Function of u in Partial Differentiation

    Homework Statement The function f(x,y) satisfies the d.e. y{\partial f \over \partial x} + x{\partial f \over \partial y} = 0 By changing to new vars u = x^2-y^2 and v=2xy show that f is a function of x^2-y^2 only. Homework Equations \frac{\partial }{\partial x}=\frac{\partial...
  50. K

    Finding Partial Derivatives with Implicit Differentiation

    Homework Statement Use implicit differentiation to find ∂z/∂x and ∂z/∂y yz = ln(x + z) The Attempt at a Solution I came up with (x+2)/(x+2)(1-xy-yz) Could someone please help me solve this. I know to treat y as a constant and to multiply all the derivatives of z by ∂z/∂x
Back
Top