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

    Applications of Differentiation

    Homework Statement A vehicle tunnel company wants to raise the tunnel fees. An expert predicts that after the increase in the tunnel fees, the number of vehicles passing through the tunnel each day will drop drastically in the first week and on the t-th day after the first week, the number...
  2. K

    Partial Differentiation in free Schrodinger Equation

    Hello again! This time I have another calculus question for you, coming straight out of my study of the free Schrodinger equation, since I am not that experienced with that kind of derivative. It all starts with a given wavefunction (which I think is 2-dimensional,correct me if wrong)...
  3. S

    Find the derivative using Logaritmic Differentiation

    y = (sinx)2x LNy = 2xLN(sinx) + (1 over sinx)(cosx)(2x) Answer y' = (sinx)2x [2cosx over sinx + 2xcotx] and y = (cosx)cosx i did it the same way as above Answer i got was y' = (cosx)cosx [ (-sinx)(cosx) + sinx] am i anywhere right?
  4. P

    Partial Differentiation Question

    I have a basic question about taking partial derivatives. Say I have a function of 3 variables and i want the derivative of only one. Do I take the derivative of the one variable and HOLD THE OTHER TWO CONSTANT? Or, do I take the derivative of the variable and TREAT THE OTHER TWO AS...
  5. S

    Logarithmic Differentiation

    y = (sin2x)3(x4-4x)6 divided by (cosx) + e3x i came out with an answer y' = (sin2x)3(x4-4x)6divided by (cosx) + e3x [3cot2x + 24x3-24 divided by x4-4x + Tanx + 3x could someone tell me if I am right? i don't know if this is what I am supose to do, if you want me to write out...
  6. B

    Differentiation Question - Chain Rule

    Homework Statement Differentiate y = \left(\frac{x+2}{\sqrt[3]{x}}\right)3 Homework Equations -Chain Rule -Quotient Rule -Power Rule -Product Rule? The Attempt at a Solution First I got rid of the fraction by taking the negative of x^3, and then used the chain rule to differentiate...
  7. H

    Implicit Differentiation Question

    Homework Statement Prove that \frac{dy}{dx}=\frac{y}{x} for \sqrt{\frac{x}{y}}+\sqrt{\frac{y}{x}}=10 x is not equal to y which is not equal to 0 The Attempt at a Solution Tried all the normal methods but none seem to work...anyone have any ideas?
  8. T

    Finding a and b for y = ax^2 + bx Passing Through (2,4) with Gradient 8

    Homework Statement The curve y = ax^{2} + bx passes through the point (2,4) with gradient 8. Find a and b . I have no idea how to work out a and b , do I use simultaneous equations? Homework Equations The Attempt at a Solution I have no idea how to work out a and b , do I use simultaneous...
  9. P

    How do I solve for y' in implicit differentiation problems?

    Homework Statement Find derivative of y with respect to x. Sin(xy) = Sinx Siny Homework Equations The Attempt at a Solution Use chain rule (product rule for inner function) to differentiate the left. Use product rule to differentiate the right and I get the following...
  10. C

    Logarithmic Differentiation with Respect to y

    Homework Statement I am trying to differentiate log((x+(x^2+y^2)^0.5)/(-x+(x^2+y^2)^0.5)) with respect to y Homework Equations I know that d/dx of ln(x) = 1/x but i am getting really confused when it comes to differentiating wrt to y? Can I have some help please! The Attempt at a...
  11. P

    Straightforward differentiation, but think I have wrong sign somewhere

    1. Homework Statement , attempt at a solution Please see attached. I'm actually busy with a physics problem, but solving it requires that I complete this part correctly. It's straightforward differentiation, but I think I made an error with my signs somewhere and I can't for the life of me...
  12. R

    Wrong answer on Differentiation

    Homework Statement In polar coords: y = rsin(\theta) y' = dy/dt = r'sin(\theta) + rcos(\theta) \theta' If I want \partial r' / \partial y' can I just solve for r' and take the derivative of y'? so \partial r' / \partial y' = 1 / sin \theta I am hoping this is incorrect because...
  13. A

    What is the partial derivative of u with respect to t in the given equation?

    if u(x,t)=ae^-gx sin(nt-gx) where A,g and n are const.,and partial derivative of u w.r.t t= a^2[(partial derivative w.r.t x(partial derivative of u w.r.t x)] show :(1/a)[n/2]^1/2=g
  14. A

    Partial Derivative of z=[x^2 tan^-1(y/x)]-[y^2 tan^-1(x/y)] with Respect to y

    given that z=[x^2 tan^-1(y/x)]-[y^2 tan^-1(x/y)].find value of [z][xy]. where [z][xy] stand for partial derivative w.r.ty(partial derivative of z w.r.tx)
  15. M

    How Do You Differentiate the Function y = (3x^2-4)^(1/2) + (x^2+4)^(1/2)?

    Homework Statement differentiate y = (3x2-4)1/2+(x2+4)1/2 with respect to x Homework Equations y = (3x2-4)1/2+(x2+4)1/2 The Attempt at a Solution dy/dx = (3x2-4)1/2dy/dx+(x2+4)1/2dy/dx Is it correct...? for the first part let u = (3x2-4)1/2 du/dx = 6x y = u1/2 dy/du = 1/2u-1/2 dy/dx =...
  16. M

    Finding the Gradient and Solving for Zero Points on a Cubic Curve

    Homework Statement 1. Calculate the gradient of the curve y = 2x3 - 5x2 + 46x + 87 at the point where it crosses the x-axix. 2. Show by differentiation and solving a quadratic equation, that there are no points on the above curve where the gradient is zero.Homework Equations y = 2x3 - 5x2 +...
  17. T

    Unraveling the Implicit Differentiation of y=vx

    Homework Statement Consider y = 2a + ax find dy/dx dy/dx = a That is right is it not, as a is treated merly as a constantNow consider this question: Use the substitution y = vx to transform the equation: dy/dx = (4x+y)(x+y)/x² into x(dv/dx) = (2+v)² According to the mark scheme they...
  18. T

    One sided differentiation prove

    i am given two differentiable function f and g . prove that for u(x)=max(f(x),g(x)) and v(x)=min(f(x),g(x)) there is one sided derivatives ??how to put mim ,max functions into the formula of derivative formula?? f'(x)_+ = \lim_{h \to 0^+} \frac {f(x + h) - f(x)}h (one-sided derivative...from...
  19. C

    Help on logarithmic differentiation problem

    Homework Statement Use logarithmic differentiation to find the derivative of the function. Homework Equations y = (sin(x))^(ln(x)) The Attempt at a Solution I guessing the first step is raise both sides to "e", but so far I have only completed problems by taking the natural log...
  20. T

    Mvt differentiation proof question

    suppose f is a continues function on point x_0 prove that g(x)=(x-x_0)*f(x) differentiable on x_0?? calculate g'(x_0) i tried to think like this: if f(x) is continues on x_0 then lim f(x) as x->x_0 equals f(x_0) mvt says f'(c)=[f(a)-f(b)] cauchys mvt says...
  21. S

    Integration after implicit differentiation

    Homework Statement What is the integral of: y + x \frac{dy}{dx} The Attempt at a Solution I know that it is xy, after implicit differentiation. However, I cannot get it without prior knowledge of implicit differentiation.
  22. F

    Find the Derivative of f(x) = x^log(x) using Logarithmic Differentiation

    Homework Statement Find the derivative of the following function f. Homework Equations f(x)=x^log(x) The Attempt at a Solution I really don't know how to do this, as it's x to the power of a function of x.
  23. K

    Differentiation Quantum Phasis

    Homework Statement Given two quantum preparations \frac{1}{\sqrt{2}} \left( |0\rangle + | 1 \rangle \right) \frac{1}{\sqrt{2}} \left( |0\rangle - | 1 \rangle \right) Give a measurement that will distinguish between these two preparations with high probability. The Attempt at a...
  24. B

    Differential of a Function and Finding Stationary Points

    Hey I'm stuck on a problem, i have to find the differential of y=5x(2x-1)^3 and therefore find the x-coordinate of a stationary point on a graph, I use the chain rule and get the differential to be 30x(2x-1)^2 and therefore the x-coordinate to be 0.5 however my textbook says the differential...
  25. B

    Why Does My Answer Differ from the Textbook in Differentiating y = x(1+x)^0.5?

    Hey guys I am having a bit of trouble solving the following problem, differentiate y = x ((1+x)^0.5) I am using the product rule however I am getting a different answer to the back of my textbook I was wondering if anyone could help clear this up for me, thanks.
  26. J

    How Can You Prove a Symmetric Derivative Property for a Continuous Function?

    Let f be continuous on [0,1] and differentiable on (0,1) such that f(0)=f(1), prove that there exist a 0 < c < 1 such that f\acute{}(1-c) = -f\acute{}(c). thanks for any suggestions.
  27. M

    Differentiation of Trigonometric functions

    Homework Statement Let y = tan2(3x-2) Find dy/dx The solution is: 2*tan(3x-2)*sec(3x-2)*3 = 6*tan(3x-2)*sec2(3x-2) Why is it not: 6*tan(3x-2)*sec(3x-2) I am thinking: y = (tan(3x-2))2 take the power 2 down,multiply with the parentes multiply with the defferentiated parentes...
  28. J

    What is the significance of the factor of 2 in the differentiation on orbifolds?

    I'm trying to understand how Randall and Sundrum go from Eq. (9) to Eq. (10) in their RS1 paper: http://arxiv.org/abs/hep-ph/9905221 I understand that since the extra dimension \phi is periodic, we must have \frac{d^2}{d\phi^2}|\phi|\propto \delta(0) - \delta(\phi - \pi). However...
  29. D

    What is the derivative of y with respect to x at the point (2,-3)?

    Homework Statement If y^2 - 2xy=21, then dy/dx at the point (2,-3) is ? Homework Equations y^2 - 2xy=21 The Attempt at a Solution I know that I have to differentiate the function. I just do not know how to do it: implicitly or explicitly.
  30. B

    Differentiation of Vector Functions: Proving Differentiability with Chain Rule

    Homework Statement Define f(0,0)=0 and f(x,y)=\frac{x^{3}}{x^{2}+y^{2}} if (x,y)!=(0,0) Let \gamma be a differentiable mapping of R1 into R2, with \gamma(0)=(0,0)\;and\; |\gamma'(0)>0|. Put g(t)=f(\gamma(t)) and prove that g is differentiable for every t in R1 Homework Equations...
  31. B

    Differentiation of vector function

    Homework Statement suppose f is a differentiable mapping of R1 into R3 such that |f(t)|=1 for every t. Prove that f'(t)\cdot f(t)=0. I guess it is more proper to write (\nabla f)(t) \cdot f(t)=0, where (\nabla f)(t) is the gradient of f ant t. Homework Equations The Attempt at a...
  32. M

    Differentiation of Unit Tangent

    So we are given T(t) = c'(t)/||c'(t)|| as well as ||T|| = 1 We also know T(t)dotT(t) = 1 and T'(t)dotT(t) = 0 The problem asks us to find T'(t) I tried differentiating c'(t)/||c'(t)|| treating ||c'(t)|| as the square root of the dot product of c'(t) with itself. I used the product...
  33. N

    Real analysis differentiation of a real function defined by a matrix

    Homework Statement Suppose A is a real nxn matrix and f: R^n --> R is definted by f(v)=v^tAv (where v^t denotes the transpose of v). Prove that the derivative of f satisfies (f'(v))(w) = v^t (A+A^t)w Homework Equations The Attempt at a Solution I'm kinda lost here and I really...
  34. Y

    Differentiation of compression factor

    Homework Statement The problem reduces the derivative (dZ/d(1/V)) to (dZ/dV) x (dV/d(1/V)), where Z is the compression factor and v is molar volume. It further shows that it equals -V^2(dZ/dV). I don't know how they arrived at that value because by my logic it should be 1/(-V^2)...
  35. A

    Integration & Differentiation Practical Example

    hi, I want to know the practical use of Integration and Differentiation. I know what it is. I just want to know how can i explain it with a practical example. example : for Differentiation - the dy/dx can be explained that y is dependent on independent variable x. How can d2y/dx2 be...
  36. M

    Implicit differentiation - messed up somewhere

    Homework Statement find d^2y/dx^2 at (1,1) for: x^2y + x^2 -y^2 = 1 Homework Equations none The Attempt at a Solution i worked it all out but the answer I am getting is not an option. could someone show me where i made a mistake? I am not asking you to do the problem for me...
  37. D

    Differentiation on Smooth Manifolds without Metric

    Hi, I'm confused about what differentiation on smooth manifolds means. I know that a vector field v on a manifold M is a function from C^{\infty}(M) to C^{\infty}(M) which is linear over R and satisfies the Leibniz law. This should be thought of, I'm told, as a 'derivation' on smooth...
  38. F

    Rolle's Theorem differentiation

    Homework Statement Let f be continuous and differentiable on [a,b], and suppose that f attains its maximum and minimum points c and d, respectively, where c,d belong to [a,b]. Show that f ' (d) = 0 Homework Equations The Attempt at a Solution I thought about using the Mean...
  39. O

    Tricky Differentiation of Derivative

    I am having trouble remembering the correct approach here. This is in regards to deriving a governing equation for conservation of momentum for a non-Newtonian fluid. I thought about posting in engineering, but it is more of a calculus question: d/dx(((-dv/dx)^(m-1))*(dv/dx)) where we are...
  40. madmike159

    How do you differentiate x^{1/x} using the power rule and chain rule?

    I was looking at results of different numbers in the equation \sqrt[x]{x} and found out that the biggest result came when it was \sqrt[e]{e}. I know this can be re-written as x^{1/x} and that the gradient would be 0 at x = e. How would you differentiate y = x^{1/x}, I can't seem to do it using...
  41. K

    Is it possible to differentiate a complex function using the chain rule?

    Can I differentiate a complex function, like e^{-if(t)}?
  42. F

    Partial differentiation find df/dx and df/dy

    Homework Statement For the function of two variables f(x,y)=tan^-1(y/x) find df/dx and df/dy I know i just differentiate with respect to x and then to y but I'm stuck on the tan^-1(y/x) I know tan^-1(x)=1/1+X^2 when I applied this with respect to x I get 1/-1+y I think this is wrong...
  43. P

    What Gives the Complex Plane its Unique Property in Complex Differentiation?

    I saw the argument for complex differentiation today and I had a question about a 'well known' aspect of the argument. My professor said something like this (at least a version of it): Derivatives on complex variables are defined in the usual way. However, in the complex plane, delta(z) may...
  44. C

    Differentiation of dot product using cartesian components

    Homework Statement Show using cartesian components that d/dt(a.b)=(da/dt).b+a.(da/dt) The Attempt at a Solution a= axi+ayj+azk b=bxi+byj+bzk a.b=axbx+ayby+azbz d/dt(a.b)= d/dt(axbx+ayby+azbz)
  45. L

    What is the Shadow Speed Function for a Walking Man and Child?

    Homework Statement A man 6 feet tall walks at a rate of 5 feet per second toward a streetlight that is 30 ft high. The man's 3 ft tall child follows at the same speed, but 10 feet behind the man. At times, the shadow behind the child is caused by the man, and at other times, by the child...
  46. L

    Partial differentiation & complex analysis

    Homework Statement Let Δf= d^2f/dx^2+ d^g/dy^2 (laplace equation - Partial Derivatives) Show Δ(f(g(z))= Mod(g'(z))^2 * Δf(w,v) where g(z)=w(x,y)+v(x,y)i Homework Equations we propably need to use cauchy riemman equations: dw/dx = dv/dy and dw/dy = - dv/dx and chain rule The Attempt...
  47. A

    Help with 1 quick implicit differentiation problem

    Homework Statement what is the implicit differentiation ? Homework Equations 2sin(x)cos(y)=1 The Attempt at a Solution d/dx[2sin(x)cos(y)]= d/dx[1] 2cos(x)*-sin(y)*dy/dx=0 I haev a bad feeling i did this wrong...
  48. U

    Implicit differentiation homework

    hi i couldn't solve this question i think there is a mistake in it anyone can check it please ? http://img296.imageshack.us/img296/3716/13055173zr3.png
  49. J

    How Can You Simplify the Derivative of Ln(x + 1/x)?

    Hi all, I have to differentiate Ln(x+\frac{1}{x}) where I first differentiate Ln and than multiply by the differentiation of the inner function 1/(x+\frac{1}{x})*(1-\frac{1}{x^2} which I simplify to \frac{x}{x^2+1}*(1-\frac{1}{x^2}) \frac{x}{x^2+1}-\frac{1}{x*(x^2+1)}...
  50. M

    Solving for f '(x) using the chain rule

    Homework Statement f(x)= x^2(x-2)^4 solve for f '(x) Homework Equations f(x) = x^2(x-2)^4 The Attempt at a Solution 4x^2(x-2)^3 The answer is given in the book as 2x(x-2)^3(3x-2) i'm not following any progression that gets me to that solution regardless of how many times I...
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