What is Derivation: Definition and 1000 Discussions

In cryptography, a key derivation function (KDF) is a cryptographic hash function that derives one or more secret keys from a secret value such as a main key, a password, or a passphrase using a pseudorandom function. KDFs can be used to stretch keys into longer keys or to obtain keys of a required format, such as converting a group element that is the result of a Diffie–Hellman key exchange into a symmetric key for use with AES. Keyed cryptographic hash functions are popular examples of pseudorandom functions used for key derivation.

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  1. ChrisBrandsborg

    Find the derivative of a function

    Homework Statement E(t) = 100te1+cos((2π*t)/365 What is the derivative of this function? Homework EquationsThe Attempt at a Solution 100*e1+cos((2π*t)/365) + 100t*e1+cos((2π*t)/365) * -(2π/365)sin(2πt/365) I have tried to use the rules for derivative of products, and also used the chain rule.
  2. Battlemage!

    B Deriving P=γ(u)mu: A Relativistic Momentum Exercise

    Okay, this is going to sound weird. I know how to get relativistic energy using calculus and the assumption that momentum is γ(u)mu, but I haven't ever been able to do it without assuming P = γ(u)mu as a given. I wanted to see how close I could get to deriving relativistic momentum strictly...
  3. P

    Cauchy Momentum Equation Derivation

    From "Cauchy Momentum Equation" on Wikipedia, The main step (not done above) in deriving this equation is establishing that the derivative of the stress tensor is one of the forces that constitutes Fi This is exactly what I am having trouble grasping. It's probably something simple and...
  4. Tazerfish

    B Derivation of time dilation without light clocks

    In the way I was taught about special relativity, time dilation is like the fundamental building block from which you derive things like relativistic mass and length contraction. So it has always struck me as quite odd, that the derivation of time dilation (in some sense the basis of special...
  5. N

    I Re-derive the surface area of a sphere

    Hey everyone, I've been stuck on this one piece of HW for days and was hoping someone could help me. It reads: The surface area, A, of a sphere with radius R is given by A=4πR^2 Re-derive this formula and write down the 3 essential steps. This formula is usually derived from a double...
  6. jdawg

    Derivation of Hydrostatic Equations Fluids

    Homework Statement I'm having a little trouble understanding how to derive the hydrostatic equations for fluid mechanics! My professor showed the derivation with respect to y in class, and it kind of made sense to me. Now I'm trying to see if I can derive the equation with respect to z and x...
  7. R

    Pressure on an open piston (derivation)

    Homework Statement http://imgur.com/a/QY1Fs Homework Equations F=dp/dt P=F/A The Attempt at a Solution I do not have the answer to this problem. Its not for homework so i won't be getting it either. I don't think my solution is correct though Let us consider a particle with speed V(x)...
  8. K

    Proof -- motion under a central force in text Symon Mechanics

    1. The derivation In a 3-dim space,a particle is acted by a central force(the center of the force fixed in the origin) .we now take the motion entirely in the xy-plane and write the equations of the motion in polar coordinate how can i derive from these equation that T(kinetic...
  9. R

    Doppler effect of a satellite (extended)

    Homework Statement http://www.physics.ox.ac.uk/olympiad/Downloads/PastPapers/BPhO_Paper3_2004_QP.pdf question 3. Should i post a picture of it if its more appropriate ? Note: I'm expected to do this in about an hour [Mentor note: Image of the relevant portion of Q3 inserted] Homework...
  10. B

    Volume magnetization currents - derivation confusion

    Hello there, I've just been learning about surface magnetization currents circulating around hypothetical square loops. Since the magnetization is uniform the circulation currents cancel where the square loops are adjacent to one another and it can therefore be said that the current circulates...
  11. Babbeus

    I Lorentz derivation of length contraction in electrodynamics

    Here is a quote from this website: My question is: is this derivation of length contraction considered to be sound and correct today? Are they treated in modern textbooks?
  12. Boon

    A Fréchet derivative derivation

    In Stone & Goldbart's Mathematics for Physics, in section 1.2.1 on the Calculus of Variations, they derive the Fréchet derivative. Part of the derivation is as follows: Equation 1: J[y + εη] - J[y] = ∫ { f(x, y + εη, y' + εη') - f(x, y, y') } dx Equation 2: J[y + εη] - J[y] = ∫ { εη ∂f/∂y + ε...
  13. R

    Hard Momentum problem (Force on blades for turbine)

    Homework Statement Here it is http://imgur.com/a/Wltb0 Homework Equations F=dP/dt Cosine rule The Attempt at a Solution For the first part of the question I'm not exactly sure what the resultant of these vectors represent. First i thought they represented the relative speed of water to the...
  14. informatory

    Why Can't I Reply on One Specific Question?

    Hello there :)
  15. A

    I Derivation of E.M. Stress Energy Tensor

    From Carroll (2004) It is possible to derive the Einstein Equations (with ##c=1##) via functional variation of an action $$S=\dfrac{S_H}{16\pi G}+S_M$$ where $$S_H= \int \sqrt{-g}R_{\mu\nu}g^{\mu\nu}d^4 x$$ and ##S_M## is a corresponding action representing matter. We can decompose ##\delta...
  16. R

    Filament lamp model (derivation)

    Homework Statement State and use simple assumptions to show that ' Power is proportional to V^5' is the expected relationship for a pure tungsten filament bulb. Homework Equations V=IR I=dq/dt Q=mcT The Attempt at a Solution I tried to use a simple model where the rate of heat loss is...
  17. M

    B Schwarzschild Metric Derivation?

    Hi, I was wondering if anybody could help me understand the derivation of the Schwarzschild metric developed by the author of mathpages website. Rather than reproduce all the equations via latex, I have attached a 2-page pdf summary that also points to the mathpages article and explains my...
  18. H

    I Derivation of Euler-Lagrange equation with change of coordinates

    Why isn't ##\frac{\partial L}{\partial t}\frac{\partial t}{\partial \dot{q_m}}## included in (5.41), given that ##L## could depend on ##t## explicitly?
  19. Q

    A Derivation of Black Hole Entropy: Hawking & Beckenstein's Arguments

    I am looking to walk trough hawking and beckenstien's arguments for the proportionality of bh entropy to surface area to better understand black hole entropy. Does anybody know where I can find this calculation? I have taken relativity and qft so I am comfortable with this level of difficulty.
  20. S

    Can't get this tension derivation........

    Ok guys, i just don't seem to know anything about tension, i thought that it would always equal the weight that is suspended from the rope...But that does not seem to be the case...and also i don't get the issue of its direction. Anyways, suppose we have an atwood machine and two unequal masses...
  21. MrDickinson

    I Can someone me simplify this expression....

    lim_(h->0^-) (e^(x+h)/((x+h)^2-1)-e^(x+h)/(x^2-1))/h = -(2 e^x x)/(x^2-1)^2 I know how to differentiate the expression using the quotient rule; however, I want to use the limit definition of a derivative to practice it more.This desire to practice led me into a trap! Now I just can't simplify...
  22. P

    I Why do we differentiate in physics and why twice?

    I have a basic understanding of the reason why we look for derivative or integration in Physics, based on the water flow example, where integration is the process of accumulating the varying water flow rate "2x" , while we reverse to the water flow rate by differentiating " x squared " the...
  23. H

    Magnetic field/circular motion equation derivation

    How would you derive f=BQ/2pim ? I've got as far as F=BQv, but now I don't know which centripetal force equation to use; either F=mv2/r or F=mw2r Update: no worries I've done it
  24. I

    I Great Circle Distance Derivation

    I derived the shortest distance between two points on a spherical surface (Great Circle Distance) , using the definition of the spherical coordinates and the dot product of the position vectors r1 and r2 where r1 = ( R cosθ1 cosφ1 , R cosθ1 sinφ1 , R sinθ1 ) r2 = ( R cosθ2 cosφ2 , R cosθ2 sinφ2...
  25. T

    B Derivation of g Factor and Missing Basic Steps in Calculation

    I was just going through the calculation to go from the top line to the bottom and was just not arriving at the same result. Working backwards and just looking at the first term (i.e. the one with coefficient ##g_L## I get): ## \frac {J^2 + J + L^2 + L - S^2 - S}{2(J^2 + J)} = \frac {L^2 + S^2...
  26. Clever Penguin

    B Deriving Special Relativity Formulae Steps

    I was bored, so I decided to derive the special relativity formulae. I drew the following diagram of a light clock: In order to find t, I did sinθ=d/ct Which gives tsinθ=d/c Which gives t=d/csinθ If v = 0, vt = 0, and θ = 90 sin90 = 1 t = d/csinθ = d/c We call this t0If v is greater than 0, vt...
  27. D

    FLP: Derivation of reflection coefficient

    In Vol. I Ch.33 of Feynman's Lectures (http://www.feynmanlectures.caltech.edu/I_33.html), 33-6, the reflection coefficient as a function of angle was derived. I am confused about the part where it said the component of A perpendicular to B (Acos (i+r)) has the right polarisation to produce B...
  28. J

    A Deriving Einstein's Equation: Calculating ##R_{00}##

    Going through Carroll's book, he is deriving Einstein's equation by looking at what it should reduce to in the Newtonian limit. Part of this process is in calculating ##R_{00}## (the ##00## component of the Ricci tensor). So he let's ##g_{\mu \nu} = \eta_{\mu \nu} + h_{\mu \nu}## where ##h## is...
  29. J

    B Derivation of E=Mc2? For the common man

    Ok this is perhaps the single most famous equation known to man. And I have basically zero idea how it came to be. I have a slight background in classical physics (a couple college classes) I know it states that energy is equal to mass multiplied by the speed of light squared. I have tried to...
  30. F

    Derivation of potential of two closed curves s and s'

    I am reading Maxwell's "a treatise on electricity and magnetism" and I came across a formula of "potential of two closed curves s and s' " ##M= \iint\dfrac{cos\varepsilon}{r} dsds'## where: ##M=## potential of two closed curves s and s' ##\varepsilon=## angle between elements ds and ds'...
  31. Muthumanimaran

    Derivation of Sudarshan-Glauber P function

    Homework Statement It is not a problem, But I am doing a coursework on Quantum Optics on my own. The following derivation is for P-function in Quantum optics from the book Quantum Optics by Marlan O.Scully and M. Suhail Zubairy. I attached the Image of the derivation with this Question...
  32. L

    Derivation of Lagrange's eqs

    Homework Statement So I'm deriving Lagrange's equations using Hamilton's principle which states that the motion of a dynamical system follows the path, consistent with any constraints, that minimise the time integral over the lagrangian L = T-U, where T is the kinetic energy and U is the...
  33. F

    Confusion in Maxwell's derivation of Ampere's Force Law - II

    I am reading Maxwell's "a treatise on electricity and magnetism, Volume 2, page 156" about "Ampere's Force Law". I have some confusion in the following pages: My question is of two parts: 1.Equation 20, i.e. ##P=\dfrac{B+C}{2r}## is the outcome of special case (i.e. l=1, m=0, n=0) But in...
  34. mertcan

    A Why Do Torsion Tensor Derivations Differ Between Sources?

    hi, I looked up torsion tensor derivation on 2 different books, and encountered 2 different situations, so my mind has been confused. For the first image, I could totally understand how torsion tensor was derived, but for the second image although there are similar things, I can not make a...
  35. F

    Confusion in Maxwell's derivation of Ampere's Force Law

    Hi everyone here. I have my question in the following attached pdf file
  36. ShayanJ

    Derivation of rotation formula in a general coordinate system

    Homework Statement [/B] In a set of axes where the z axis is the axis of rotation of a finite rotation, the rotation matrix is given by ## \left[ \begin{array}{lcr} &\cos\phi \ \ \ &\sin\phi \ \ \ &0 \\ & -\sin\phi \ \ \ &\cos\phi \ \ \ &0 \\ &0 \ \ \ &0 \ \ \ &1 \end{array} \right]##...
  37. K

    I Gradient Derivation: Simplifying Directional Derivatives

    Hello, could anyone provide me the derivation of this? I was not sure how it is possible to get to the point that directional derivative can be broken down into the linear sum of the equation in the attatched file.
  38. Andreas C

    Centripetal acceleration derivation

    Ok, so I'm a bit confused by the derivation of a=v^2/r in Feynman's "Six Not-So-Easy Pieces". In pages 17-18, it is stated that "The other component of acceleration, at right angles to the curve, is easy to calculate, using Figures 1-7 and 1-8. In the short time Δt let the change in angle...
  39. T

    I Derivation of equations using tensor

    http://hitoshi.berkeley.edu/221a/tensorproduct.pdf I was following the above pdf and got through most of it but am not quite understanding how (41), (42), and (43) are derived. It appears that (31) and (41) are representing the same states and are still orthogonal, but how exactly is (41)...
  40. T

    I Derivation of planetary orbit equation with Lagrangian

    I am stuck at this part page 1, $$\frac{\partial{L}}{\partial{\dot{φ}}}=\mu{r^2}\dot{φ}=const=l------->\dot{φ}=\frac{l}{\mu{r^2}}......(8)$$ Why is this a constant? Isn't r and dφ/dt variables of time? Source: http://www.pha.jhu.edu/~kknizhni/Mechanics/Derivation_of_Planetary_Orbit_Equation.pdf
  41. S

    Why is 2L used as the distance in the derivation of 1/3nMc^2 = nRT?

    In the derivation the first step used F=Δmv/t and for t, they used t=2L/v where L is the distance between one end to the other end of the wall. But I don't understand why we use 2L as the distance. Isn't the force exerted by that molecule only for the very short period where the molecule is in...
  42. bananabandana

    I Confusion With Derivation of Fresnel Equations

    Okay, so I'm working with the diagrams above. ##i## denotes incident, ##r## reflected, and ##t## transmitted. -We're working in two HIL dielectrics. Incoming and outgoing waves are of form ##Aexp[i(\vec{k}\cdot\vec{r}- \omega t) ##. As I understand it, Maxwell's equations give four boundary...
  43. T

    I Planck's 1st Derivation of Planck's Law?

    My information comes from: http://www.cems.uvm.edu/~tlakoba/AppliedUGMath/notes/lecture_13.pdf Quote A: Quote B: Quote C: Quote B and Quote C concern Planck's Law, not Wien's Law. I know how Planck derived it as mentioned in Quote C.However, what are the "phenomenological Thermodynamics"...
  44. S

    Centripetal Acceleration formula derivation

    Hello, This is a very basic question. I am sure I am doing something wrong in the derivation as shown in the picture. But I am not able to find out where I am doing it wrong. It would be very helpful if you can pls. let me know what I am doing wrong here. Thanks
  45. T

    Derivation of the Overall Mass Transfer Coefficient

    Homework Statement The problem requires me to find the overall mass transfer coefficient or Kg. Homework Equations $$N_{1}=\frac{1}{\frac{1}{k_{p}+\frac{H}{k_{x}}}}(p_{1}-Hx_{1}), (1)$$ $$N_{1}=k_{p}(p_{1}-p_{1i}), (2)$$ $$N_{1}=k_{x}(x_{1i}-x_{1}), (3)$$The Attempt at a Solution So, I...
  46. V

    2 Body Radial Equation, Effective Potential derivation

    According to my textbook, in the derivation for the effective potential U_{eff}, starting with the Lagrangian L = \frac{1}{2}\mu(\dot r^2 +r^2\dot\phi^2) -V(r), substituting into Lagrange's equation gives \mu\ddot r = -\frac{\partial V}{\partial r} + \frac{l^2}{\mu r^3} =...
  47. S

    B Help understanding this derivation of relativistic Doppler

    I'm looking at George Smoot's derivation on pp. 2-3 here: http://aether.lbl.gov/www/classes/p139/homework/five.pdf It's elegant and succinct, but I'm having trouble understanding the very last step. Using the Lorentz transformation, he gets this relationship: ##dt = dt^\prime \gamma (1 +...
  48. A

    A Deriving DOS: Solve the Mystery of the 2x Factor!

    Hi guys, I have a very particular question on the derivation of DOS. For a particle in an infinite box k=π/L. However, when deriving the density of states, all textbooks use k=2π/L Now you could argue that they account for spin degeneracy, but its not that! Because in the textbooks that...
  49. K

    Ideas on how to easily solve this long derivation?

    Mod note: Moved from a Homework section 1. Homework Statement I want to solve: ∇2E, for E = exp(ikr)/r, where r = √x2+y2+z2 Thus I must solve: d2E/dx2+d2E/dy2+d2E/dy2 The derivatives themselves are simple, but very time-consuming! Can you think of any tricks I can use to simplify the calculation?
  50. S

    I Angular momentum ladder operator derivation

    In the Griffiths textbook for Quantum Mechanics, It just gives the ladder operator to be L±≡Lx±iLy With reference to it being similar to QHO ladder operator. The book shows how that ladder operator is obtained, but it doesn't show how angular momentum operator is derived. Ive searched the...
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