Differentiate Definition and 226 Threads

Cellular differentiation is the process in which a cell changes from one cell type to another. Usually, the cell changes to a more specialized type. Differentiation occurs numerous times during the development of a multicellular organism as it changes from a simple zygote to a complex system of tissues and cell types. Differentiation continues in adulthood as adult stem cells divide and create fully differentiated daughter cells during tissue repair and during normal cell turnover. Some differentiation occurs in response to antigen exposure. Differentiation dramatically changes a cell's size, shape, membrane potential, metabolic activity, and responsiveness to signals. These changes are largely due to highly controlled modifications in gene expression and are the study of epigenetics. With a few exceptions, cellular differentiation almost never involves a change in the DNA sequence itself. Although metabolic composition does get altered quite dramatically where stem cells are characterized by abundant metabolites with highly unsaturated structures whose levels decrease upon differentiation. Thus, different cells can have very different physical characteristics despite having the same genome.
A specialized type of differentiation, known as 'terminal differentiation', is of importance in some tissues, for example vertebrate nervous system, striated muscle, epidermis and gut. During terminal differentiation, a precursor cell formerly capable of cell division, permanently leaves the cell cycle, dismantles the cell cycle machinery and often expresses a range of genes characteristic of the cell's final function (e.g. myosin and actin for a muscle cell). Differentiation may continue to occur after terminal differentiation if the capacity and functions of the cell undergo further changes.
Among dividing cells, there are multiple levels of cell potency, the cell's ability to differentiate into other cell types. A greater potency indicates a larger number of cell types that can be derived. A cell that can differentiate into all cell types, including the placental tissue, is known as totipotent. In mammals, only the zygote and subsequent blastomeres are totipotent, while in plants, many differentiated cells can become totipotent with simple laboratory techniques. A cell that can differentiate into all cell types of the adult organism is known as pluripotent. Such cells are called meristematic cells in higher plants and embryonic stem cells in animals, though some groups report the presence of adult pluripotent cells. Virally induced expression of four transcription factors Oct4, Sox2, c-Myc, and Klf4 (Yamanaka factors) is sufficient to create pluripotent (iPS) cells from adult fibroblasts. A multipotent cell is one that can differentiate into multiple different, but closely related cell types. Oligopotent cells are more restricted than multipotent, but can still differentiate into a few closely related cell types. Finally, unipotent cells can differentiate into only one cell type, but are capable of self-renewal. In cytopathology, the level of cellular differentiation is used as a measure of cancer progression. "Grade" is a marker of how differentiated a cell in a tumor is.

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  1. A

    How do you differentiate implicitly with three variables (x,y,a)?

    Homework Statement Find the equation of the tangent line to the following curve at the indicated point: x^(2/3) + y^(2/3) = a^(2/3) at (a, 0) Homework Equations Power rule Chain rule The Attempt at a Solution (2/3)x^(-1/3) + [(2/3)y^(-1/3)](dy/dx) = [(2/3)a^(-1/3)](da/dx)...
  2. fluidistic

    How Can I Improve My Understanding of Differentiating Equations?

    My friend came up with the following: 2x=1 \Rightarrow \frac{d}{dx}(2x)=\frac{d}{dx}1 \Rightarrow 2=0. Shamefully I do not see what's wrong with this reasoning! Can someone help me? :)
  3. C

    Differentiate e^fx: Solving 2xe^(2x)

    f(x)= xe^(2x) So I applied the product rule (f • g) = x • e(^2x) + e^(2x) • 1 = xe^(2x) + e^(2x) =2xe^(2x) And got this as my final answer. Would I need to use chain rule? Did I do this correctly?
  4. J

    Differentiate a thermo equation

    Homework Statement Air at 300K(=T_s) flows over a flat plate maintained at 400K(=T_f). At a particular location on the plate, the temperature distribution in the air measure from the plate surface is given by T(y)=(T_s-T_f)exp[-22,000*y(m)]+T_f Q.Determine the conduction heat flux through...
  5. N

    Why specific heat at near critical point equals differentiate twice Gibbs energy?

    Please teach me this: Why specific heat near critical point equals differentiate twice Gibbs free energy with respect to temperature, but not differentiate once with respect to temperature as usually doing. Thank you very much in advance.
  6. 1

    Differentiate the given function using implicit.

    Homework Statement 2x^3 - 8xy + y^2 = 1 Homework Equations The Attempt at a Solution d2x^3/dx - d8xy/dx + dy^2/dx = d1/dx 6x^2 -8(y) + dy/dx(-8x) + 2y(dy/dx) = 0 6x^2 - 8y -8x(dy/dx) + 2y(dy/dx) = 0 I am stuck and can't seem to go further. Someone help?
  7. C

    How to differentiate functions with x in their exponents

    I'm not sure how to differentiate y with respect to x for: y = (7x^2)^[x^2] Any ideas?
  8. P

    Why are they called differentiate & integrate ?

    Why are they called "differentiate" & "integrate"? I was wondering why. When we differentiate, don't we result in an equation that describes the slopes of many other equations ( + C ) ? So, we'd be "integrating" many equations, different from each other by C, into a single description...
  9. J

    Differentiate y=2t+3 and x=t^2 -t

    Homework Statement Differentiate each function and if possible express your answer in factoring form y=2t+3 and x=t^2 -t Homework Equations The Attempt at a Solution im really lost on this question but this is what i did so far x=t(t-1) x/t-1=t so: y=2(x/t-1)+3 but now I am...
  10. P

    How do you differentiate a^x with regard to x?

    Homework Statement Hi, this is part of a stats problem, in the solutions they go from: d/dc of ln(1-0.5^c) then next line they have: ln(0.5).[0.5^c]/(1-0.5^c) I don't understand how they did this! Homework Equations The Attempt at a Solution So, I know that the...
  11. A

    What is the Derivative of 3(2x^2 + 1)?

    Differentiate the following: 3(2x2 +1 ) Heres my attempt 4x.3(2x2+1)^0 anything the the power of 0 = 1 So we have: 12x.(1) = 12x Is this correct?
  12. N

    How to Find the Derivative of an Integral Using Differentiation

    Homework Statement Hi Say I have for example f(x) = \int_0^x {e^{ - (x - x')} g(x')\,dx'} Then is it correct that the derivative of f(x), f'(x), is given by f'(x) = g'(x) - g(x) obtained by differentiating the integrand, and evaluate the result at x'=x? Best.
  13. J

    Quotient Rule (In what order do you choose which to differentiate)

    Homework Statement The Derivative of x-2/(x^2-1) Can you show me how to get the derivative using the quotient rule and tell me if the order matters? I always thought that the order never mattered until I got a wrong graph because it seems I got the wrong derivative. Homework...
  14. 1

    Differentiate the following, please

    If you would be so kind, I missed today's lecture and do not even know where to begin. i) x = 3t^3 + 6√t + 3/t^2 ii) y = 3sin 2x + 5cos(4x)
  15. L

    Differentiating Integrals w/ Respect to x: Tips & Tricks

    Homework Statement Differentiate the following functions with respect to x. a) \int (t2 + cos(t7))/(1 + t4) dt [0, x] b) \int (t2 + cos(t7))/(1 + t4) dt [2, x] c) \int (t2 + cos(t7))/(1 + t4) dt [0, sin x] d) \int (t2 + cos(t7))/(1 + t4) dt [x, sin x] e) \int (x2 + cos(t7))/(1...
  16. 1

    Differentiate the given function

    Homework Statement differentiate the following funtion: g(x) = x^3*e^-1/x + 3^x*ln(1/x) Homework Equations chain rule and product rule The Attempt at a Solution x^3*d/dg(e^-1/x)d/dg(x)^3 + 3^x sorry...i am very confused!
  17. N

    Finding the Derivative of (2/x)^(1/x)

    Homework Statement Find (2/x)^(1/x). Simplify your answer. Homework Equations The Attempt at a Solution I let y = (2/x)^(1/x) lny = ln(2/x)^(1/x) lny= ln(2/x)/x However, I get stuck here and don't know whether I should use e on both sides to get y by itself or to use implicit...
  18. N

    How to Find the Derivative of f(t) with Respect to t

    f(t) = K(t) - K(t-T) I want to find \frac{df}{dt} i'm unsure of the notation, does the 3rd term represent K as a function of t-T :facepalm:? I know the 2nd term is showing K is a function of time otherwise it would be written simply Kt, but unsure of the 3rd term. I'm confused :S If the...
  19. J

    How Do You Differentiate an Integral with Variable Limits and Parameters?

    Homework Statement If f(x) = \int_{x^2}^{3x} \sqrt{t^3 + x^3} dt then find the expression for f'(x) Homework Equations The Attempt at a Solution Usually I would use the FTC, but since there the variable x occurs in the integrand, I don't know how to differentiate this. Any help?
  20. L

    Differentiate the following functions?

    Homework Statement Differentiate the following functions: a) x3cos(5x)sin(cubedroot(x) + 2) b) tan(1 + cos2(xsin3(x2 + 1))) c) (x2 + (x2 + (x2 + 1)-1)-1)-1Homework Equations The Attempt at a Solution These are the most terrifying questions I have seen thus far in my textbook... I have no...
  21. A

    How to differentiate 6^(sin(pix))

    Homework Statement Find the derivative to: y = 6^{sin(\pi x)} Homework Equations You tell me The Attempt at a Solution I am quite surprised that we are asked to do this when we are just learning the chain rule. We have not learned how to differentiate something like a^x yet...
  22. A

    Differentiate inverse (e^x + ln x )

    Homework Statement Let f(x) = ex + ln x Find (f-1) ' (e) Homework Equations let y = f-1 x The Attempt at a Solution I tried finding the inverse of f(x) but got stuck. I arrived at: x = ey + ln y How do I make y the subject of formula?
  23. E

    Is there a way to differentiate between numbers

    like N=5053=163*31 and N=169*37=6253 if we do not know the factors and if we do not want to factor them. They both have the same last two digits. I can't think of any test to apply to this kind of numbers ( it's in fact a family of numbers that share the same last two digits but are product of...
  24. B

    Troubleshooting Differentiation of x over Root x

    I tried to use tex code but it seems to be caching the image on preview, so anyway dy/dx ( x / root x) = 1 / ( 1/2 x^(-1/2) ) however the answer given to me is just ( 1/2 x^(-1/2). What's gone wrong? Spent an hour on this and now unsure if my algebra is wrong. And the tex code that I...
  25. A

    Understanding the Derivative of F=Fi (sin ct)

    Homework Statement differentiate F=Fi (sin ct) The Attempt at a Solution Fi is a constant = Fi (-cos ct)(c) That is the solution I keep getting, but my buddy keeps getting Fi (- cost ct)/c in other words, he thinks - cost ct should be divided by c, anyone care to...
  26. F

    Differentiate, Evaluate Intergral

    Differentiate: (6-xe^x)/(x+e^x)=... Evaluate Intergral: (2u^5-8u^3+5u^2)du, from lower limit -1 to higher limit 0. (i got 10/3 for some reason...) (u^7+6u^13)/u^9 du, from lower limit 1 to higher limit 2. (n i got 47 for this..) I tried these a few times but my answer is still...
  27. D

    How to differentiate y = 8 ln x - 9 x with respect to x^2?

    How to differentiate y = 8 ln x - 9 x with respect to x^2?
  28. J

    Differentiate e^(-1/2 x) sqrt(1 + 2x) - troubles

    the curve y = e^ −1/2x √(1 + 2x) please differentiate this equation i am having some problem.. i want to check my answer My answer : e^-1/2x { (1+2x )^-1/2 + (1+2x)^1/2 (-1/2) } In fact i need to find the x-coordinates and according the booklet the answer of the x-coordinate is 0.5...
  29. N

    Differentiate: f(x) = (x)(√(x^2+5))

    Homework Statement Differentiate. f(x) = (x) (square root of (x2+5)) Homework Equations The Attempt at a Solution f(x) = (x) (square root of (x2+5)) =(x)(x2+5)1/2 f'(x)=(x)1/2(x2+5)-1/2(2x)+(1)(x2+5) =x3/(x2+5)1/2+(x2+5)1/2 I'm having problems simplifying. The...
  30. E

    How to compute the derivative with respect to a vector in index notation?

    Dear all; I need to find this derivative: \frac{\partial}{\partial \mathbf{a}}\left(E-2\,\mathbf{a}^{\text{T}}\,E[\mathbf{s}]+\|\mathbf{a}\|^2\right) where boldface letters indicates column vectors, the superscript T indicates transpose, and ||.|| is the norm of a vector. Thanks in...
  31. M

    Understanding Differentiation with x: ln and Exponents

    Homework Statement 1) ln { (x^2+x+1) / ( x^2-x+1) } here ln = natural log 2) x^2+x^(2y)=c here c=constant Homework Equations The Attempt at a Solution
  32. T

    Troubleshooting Differentiation Using the Long Formula

    Homework Statement I have to differentiate using the long formula [f(x+h)-f(x)] / (h). Homework Equations f(x) = (1)/(2+x), x=2 The Attempt at a Solution First I wrote [ (1/2+x+h) - (1/2+x) ] / (h). Then I created a common denominator in the numerator. I then made the bottom...
  33. S

    How to differentiate phenol, acetic acid, aniline & nitrobenzene

    Homework Statement The question actually contains a diagram but i don't understand how to draw it, so i'll try to describe it in words. A solution contains phenol, acetic acid, aniline and nitrobenzene. Na2CO3 is added into the solution and two layers are formed: aqueous layer A and ethereal...
  34. G

    Differentiate e^x and Trig Functions

    Homework Statement Differentiate e^x * cotx / 5sqrtx^2 [Sorry for not using the formatting things. They didn't seem to be working for me, and this is urgent!] Homework Equations The quotient rule seems like that's the way to go... The Attempt at a Solution At first I tried using...
  35. T

    Transforming Log & Exp Equations: Differentiate wrt x

    Write the following log equations as exponential equations and vice-versa. 1.) ln 0.5 = - 0.6931 Differentiate with respect to x. 2.) y = e^x(sin x + cos x)
  36. J

    How are we able to differentiate both sides of an equation?

    Consider this equation. x^3 = x + 6 If we solve for x we'll get x=2 Now if we differentiate both sides with respect to x, we get 3x^2 = 1 If we now put x=2, we get 3(2)^2 = 12 = 1 Which is of course wrong. So how can we differentiate both sides of an equation when the value...
  37. L

    Looking for Automation System to Differentiate Distinct Sounds

    I'm currently looking for a system which can automate a part of my process. Currently, there is an operator listening for sound, which is distinct enough for the human ear. Upon hearing this sound, he shuts down the system. I would imagine that if an ear can easily differentiate the sound, a...
  38. F

    Who Can Find the Time for a Falling Object with Resistive Force?

    For a falling object, who can find the time in terms of the velocity for this journey( before reaching terminal velocity) with considering the resistive force?
  39. Y

    How to differentiate conductors and semiconductors?

    Hello everyone, I have a (simple?) question: How do you differentiate a material to be a conductor or a semiconductor? It is just only by examining the material's electrical resistivity/conductivity whether it is low or high? Because I have heard that even some metallic conductors have high...
  40. Y

    How to differentiate conductors and semiconductors?

    Hello everyone, I have a (simple?) question: How do you differentiate a material to be a conductor or a semiconductor? It is just only by examining the material's electrical resistivity/conductivity whether it is low or high? Because I have heard that even some metallic conductors have high...
  41. D

    Differentiating Trigo: 18tan^2(x)sec^2(x)

    18tan^2(x)sec^2(x) Is this correct? Product Rule I think... 18tan^2(x)sec^2(x) = (18tan^2(x))(2sec^3(x)) + (sec^2(x))(36tan^3(x)) = (36tan^3(1+tan^2(x))) + (36tan^3(1+tan^2(x))) = 2(36tan^3(1+tan^2(x))) 1 more thing is tan x = sec^2(x)? Any 1 has a list of Trigo formulas? Becoz' I am...
  42. T

    Finding dy/dx: Differentiating (4sinx)(cosy)=1 with respect to x

    . differentiate (4sinx)(cosy)=1 w.r.t x and fine dy/dx Im stuck here (4cos x)(cos y)+ (4sin x)(-sin dy/dx[y])
  43. S

    Using chain rule to differentiate x^x

    Homework Statement Use the chain rule to find (d/dx)(xx) by using the function f(y,z)=yz. Homework Equations Chain rule: \frac{dz}{dt} = \frac{\partial z}{\partial x} \frac{dx}{dt} + \frac{\partial z}{\partial y} \frac{dy}{dt} The Attempt at a Solution I honestly have no clue on how to use...
  44. F

    Differentiate TU= 4 sqr x1 + x2

    TU= 4 sqr x1 + x2 differentiate by x1 if x1=9 and x2=8
  45. G

    Differentiate an ionic from a covalent compounds

    I have come to a situation that I can hardly differentiate an ionic from a covalent compounds! Before this confusion I had firstly known that whenever I find a compound with constituents of atoms with a very large difference in electronegativity, then i just conclude that its ionic, or when I...
  46. P

    How do you differentiate & integrate e to the x?

    1.a Evaluate the following. Show all work. http://img90.imageshack.us/img90/289/problemu.png 1.b Differentiate. http://img293.imageshack.us/img293/1440/problem2.png Homework Equations ƒ b-a f(x)-g(x) The Attempt at a Solution...
  47. D

    How do you differentiate this?

    Here's the problem: Differentiate: http://www.webassign.net/www31/symImages/9/b/f70b139b79e8157ad26bf9782128ae.gif I tried this and somehow came up with 7(x^3/2) - 8(x^1/2). But that is not correct. How do you do this? I really appreciate your help. Thanks.
  48. N

    How to differentiate between single and multiloop circuits

    This is just a general question that will help me start a problem, so I have no work to show. The question is: How can you tell that a problem is a multiloop circuit? Does it correspond to the number of voltage sources (batteries) in the circuit, or is it based off of how the components of the...
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