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. S

    Derivation of gravitational redshift: Mass of a photon?

    This is not exactly a homework question. In a physics textbook, they derive an expression for gravitational redshift of a photon emitted by a star at a large distance from the source by taking photon as a mass traveling up, against a gravitational potential and hence expending its...
  2. H

    Christofell Symbols: Derivation in Schutz & Wald

    In Schutz, the christofell symbols are dervied from applying the product rule to a vector in a curvillinear basis. In Wald, the christofell symbols are dervied by making an ansatz of the form a covariant derivative must take and then imposing conditions on it like the metric covariant...
  3. I

    Help me solving a Derivation equation

    Homework Statement find the derivative of the given function: f(x)= 6 - (1/x) / x-2 Homework Equations The Attempt at a Solution the solution on the answer key is (-6x^2 + 2x - 2 ) / (x^2 (x-2)^2) i don't know how to solve it :(
  4. J

    Simple question - Derivation for obtaining Intgrating Factor

    I was wondering if somebody could clear up some confusion I have regarding this. I've been going over the derivation for obtaining the integrating factor again in my book and there is one step I don't understand. There's no point going through the whole thing from scratch, but I've got to...
  5. D

    MHB State Matrix Derivation for Orbital Mechanics

    Has anyone seen the derivation of \(\ddot{\mathbf{r}} = -\frac{\mu}{r^3}\mathbf{r}\) into state matrix form? If so, can they provide a link?
  6. gfd43tg

    Non-Ideal Op-Amp gain derivation

    Homework Statement Problem statement is in the attachment HW 5, it is problem #1. Homework Equations The Attempt at a Solution I am just stuck with a whole bunch of variables and this just looks like a complete mess
  7. T

    Derivation of Line of Best Fit

    Homework Statement Consider a set of data points: (x1, y1), (x2,y2). One seeks to find the best coefficients A and B such that the sum of squared vertical distances of the data f(x) = Ax + B is minimized. Let D = ∑[yi - f(xi]2. By requiring the derivatives of D respect to both A and B each to...
  8. W

    Derivation of formula for time dilation

    I know how to derive the lorentz time dilation equation. I am wondering how to derive the equation for gravitational time dilation: T=To(1/(sqrt(1-(2GM)/(Rc2)))
  9. A

    Derivation of drift speed question

    Homework Statement First off, this is NOT a homework problem. This is a conceptual question I have regarding the derivation of the drift velocity v_d =[(qE)/m] \tau Typically, when this formula is derived, you first calculate the acceleration of a particle in the electric field (qE/m) and...
  10. C

    Expanding delta in Field Theory Derivation of Euler-Lagrange Equations

    Every time I try to read Peskin & Schroeder I run into a brick wall on page 15 (section 2.2) when they quickly derive the Euler-Lagrange Equations in classical field theory. The relevant step is this: \frac{∂L}{∂(∂_{μ}\phi)} δ(∂_{μ}\phi) = -∂_{μ}( \frac{∂L}{∂(∂_{μ}\phi)}) δ(\phi) + ∂_{μ}...
  11. C

    Expanding delta in Field Theory Derivation of Euler-Lagrange Equations

    Every time I try to read Peskin & Schroeder I run into a brick wall on page 15 (section 2.2) when they quickly derive the Euler-Lagrange Equations in classical field theory. The relevant step is this: \frac{∂L}{∂(∂_{μ}\phi)} δ(∂_{μ}\phi) = -∂_{μ}( \frac{∂L}{∂(∂_{μ}\phi)}) δ(\phi) + ∂_{μ}...
  12. C

    Peskin and Schroeder derivation of Klein-Gordon propagator

    In page 30 of book "An introduction to quantum field theory" by Peskin and Schroeder in the derivation of Klein-Gordon propagator, why p^0=-E_p in the second step in equation (2.54). and why change "ip(x-y)" to "-ip(x-y)"? I thought a lot time, but get no idea. Thank you for your giving me an...
  13. E

    Incident Angle Limitation Derivation in Optical Fibre

    Homework Statement derive the angle of limitation sinθ=[(n2^2-n3^2)^1/2]/n1 n1 is the air out side of the fibre n2 is inside of the fibre n3 is the fibre wall Homework Equations Snells Law: n1sinθ1=n2sinθ2 The Attempt at a Solution I'm pretty stuck and don't really know...
  14. K

    Simple Derivation Maxwell Equations

    Homework Statement Derive the 2 divergence equations from the 2 curl equations and the equation of continuity. Homework Equations ∇°D=ρ ∇°B = 0 ∇xE = -∂B/∂t ∇xH = J + ∂D/∂t ∇°J = -∂ρ/∂t (equation of continuity) The Attempt at a Solution 1)∇xE = -∂B/∂t ∇°(∇xE) = ∇°(-∂B/∂t)...
  15. S

    Stat mech derivation: Covarience of energy and pressure

    Homework Statement Prove for the canonical ensemble ##\overline{(E-U)(p-\overline{p})}=kT[(\frac{\partial U} {\partial V})_{N,T} + p]## Left hand side is covariance E is energy U is internal energy, average of E p is microstate pressure $$\overline{p}$$ is average pressure V is volume N is...
  16. D

    Derivation of Laplace in spherical co-ordinates

    I have been trying to derive the Laplace in spherical co ordinates. I have attached a file which has basic equations. I am trying to get the following equation. d(phi)/dx= -sin(phi)/(r sin (theta)). I have also attached the materials I am referring to. Can someone please help me derive...
  17. E

    Derivation of Phi-Hat wrt Phi in Spherical Unit Vectors

    Homework Statement I just want to know how to get from this: ∂ø^/∂ø = -x^cosø - y^sinø to this: = -(r^sinθ+θ^cosθ) Homework Equations All the equations found here in the Spherical Coordinates section: http://en.wikipedia.org/wiki/Unit_vector The Attempt at a Solution I've...
  18. schrodingerscat11

    Derivation: Normalization condition of Legendre polynomials

    Greetings! :biggrin: Homework Statement Starting from the Rodrigues formula, derive the orthonormality condition for the Legendre polynomials: \int^{+1}_{-1} P_l(x)P_{l'}(x)dx=(\frac{2}{2l + 1}) δ_{ll'} Hint: Use integration by parts Homework Equations P_l=...
  19. G

    Simplified derivation of viscosity equation

    Homework Statement Think of a fluid between two plates at a distance d from each other in the z-direction; then slide the top plate at a constant speed v_0 in the x-direction while holding the bottom plate still. The fluid pushes back, so you need to apply a force F in order to keep the plate...
  20. M

    Derivation of Lorentz Transformation for Acceleration

    Homework Statement Starting with the Lorentz transformation for the components of the velocity, derive the transformation for the components of acceleration.Homework Equations Lorentz Transformation for position and time : ##x'={\gamma}(x - vt)## ##t'={\gamma}(t - {\frac{vx}{c^2}})## Resulting...
  21. M

    How can I derive the equation for calculating pump horsepower?

    hi everyone can anyone please give me a clue of how to derive this equation Hp= Q(gpm)* Δp(psi)/1714 Q is volumetric flow rate Δp is pressure
  22. T

    Derivation of the exponential distribution - that infinitesimal

    Hello, I've been looking at the derivation of the exponential function, here http://www.statlect.com/ucdexp1.htm amongst other places, but I don't get how, why or what the o(delta t) really does. How does it help? It's really confusing me, and all the literature I've looked at just...
  23. D

    Solving Lagrangian Derivation - Classical Mechanics by John R. Taylor

    I have been reading Lagrangian from Classical Mechanics by John R. Taylor. I have adoubt in a derivation which invloves differential calculus. I have attached snapshot of the equation , can someone please explain. Here y,η are functions of x but α is s acosntant. Please let me know if I...
  24. M

    Help with a wave equation derivation

    Hi, Apologises if I have submitted this issue into the wrong Math forum. However, I was wondering if anybody could help me with 2 steps in a derivation of an equation. Simply by way of background, the derivation is linked to formation of a superposition wave subject to a Doppler effect [1]...
  25. S

    Derivation of the quadrupole moment of gravitational wave

    Hi, Can anyone give a derivation of the quadrupole moment in the TT gauge ( Equation metioned below ) of the gravitational wave ? QijTT(x) = ∫ρ(xixj-1/3δijr2)d3x Where ρ is the matter density Thanks In Advance
  26. D

    Derivation of reflection/transmission coefficients

    Greetings! Going throught Ballentine Ch.4 and the derivation of transmission/reflection coefficients. The math seems fairly straightforward: assuming a particle in a piecewise-constant potential, the solution of the correspondent time-independent SE is a piecewise-exponential wavefunction in...
  27. B

    RC circuit with Schmitt trigger - Derivation

    In lectures I covered how a Schmitt trigger can be used in an RC circuit to determine the capacitance of the capacitor (Where the Schmitt trigger switches at 0.3V+ and 0.6V+). The equation given was that C = 1.2 R \ T (time period) Does anyone know how to derive this or where it comes from...
  28. polygamma

    MHB A derivation of the duplication formula for the Barnes-G function

    In a commentary thread DreamWeaver asked if anyone knew of a derivation of the multiplication formula for the Barnes-G function other than the almost impossible to follow derivation in Barnes' original paper. I suggested using the multiplication formula for the Hurwitz zeta function. In this...
  29. S

    Heisenberg Uncertainty Principle Derivation

    I know I have seen this before a few time done a few different ways/starting points and I am always blown away when I see it worked out. Don't know why but I love seeing this derivation. Does anyone want to post the derivation for all to see, it being done a few different ways would be great.
  30. O

    Derivation for black body radiation. What is the 2 bout?

    $${\rho}({\lambda}) d{\lambda}=E({\lambda})*f({E(\lambda}))*D({\lambda})d{\lambda}$$ $${\rho}({\lambda}) d{\lambda}$$ is density of radiative energy, $$E({\lambda})= k_BT$$ is the energy of an atom vibrate in 3D, $$f({E(\lambda}))=1$$ is the probability distribution. Equals to 1 because we...
  31. A

    This answer has been edited to fix the grammar and punctuation errors.

    Homework Statement I am supposed to show equation 6.6 on page 97 of http://www.phys.lsu.edu/~jarrell/COURSES/ADV_SOLID_HTML/Other_online_texts/Many-body%20quantum%20theory%20in%0Acondensed%20matter%20physics%0AHenrik%20Bruus%20and%20Karsten%20Flensberg.pdf I have tried to plug A and the...
  32. S

    Derivation of energy-stress tensor in GR

    Would there be a direct proof of the energy-stress tensor of general relativity? My lecturer only provides me with a simplified proof - 1. Guess the form of the tensor in special relativity in co-moving frame (ρ+p)uμuv+pημv Note that the pη00 term cancels the p in u0u0, to simplify the...
  33. G

    Derivation of Schwarzschild radius from escape velocity

    Hi, Is it pure coincidence that if you put ##c=v_e=\sqrt{2GM/R}## in the escape velocity, you end up with the Schwarzschild radius ##R=2GM/c^2##? The derivation of the escape velocity is purely classical mechanics. It involves ##E_{kin}=mv^2/2## which is incorrect in special relativity...
  34. H

    Simple harmonic motion equations derivation?

    Well I was going through class lecture notes and my professor wrote this When x = A(the maximum value), v=0: E=1/2kA^2 When v = wA, x=0: E=1/2mw^2A^2 where w = omega, A = amplitude, k = spring constant, m = mass, v = velocity and apparently both equations are equal, i would like to...
  35. M

    Derivation for Moment of Inertia of Rectangle rotated through center

    Homework Statement I need to know how to derive the equation for the moment of inertia of a rectangle rotated about an axis through its center. The rectangle has sides a and b. I know the equation to be (1/12)M(a2+b2), but I am having trouble deriving it. I have searched all over the...
  36. V

    Archived Derivation of total magnetic field with changing distance in a coil?

    Homework Statement You are a member of a research team studying magnetotactic bacteria. Magnetotactic bacteria from the southern hemisphere preferentially swim to the south along magnetic field lines, while similar bacteria from the northern hemisphere preferentially swim to the north along...
  37. N

    Minimum Energy Curve Derivation Help

    I've been trying to find the equation of the line of no strain of a bent linearly elastic beam of fixed length. (in a plane, given just its endpoints, or both the end points and the slopes at the endpoints) I imagine this problem has been solved many times, but I couldn't find a solution online...
  38. S

    Understanding the Derivation of the Quadratic Formula

    This could be seen as a rather "basic" math question, but it is a topic of curiosity for me. I'm currently a senior in high school, taking a pre-ap pre-cal/trig/AP-Calculus double blocked class. I'm absolutely fascinated by mathematics, and something of keen interest to me is the derivation of...
  39. O

    Divergence formula derivation ?

    Homework Statement How to get equation 1 from the thumbnail? h1 h2 h3 doesn't have to be constant. The most I can try is equation 2 . Please guide thanks. Homework Equations The Attempt at a Solution
  40. andrewkirk

    Seeking thorough derivation of Friedman equations

    I am looking for a derivation of Friedman's equations from the Cosmological Principle and Einstein's field equations. The text from which I am teaching myself (Schutz) does it all in two massive leaps, whose reasoning are respectively "it is easy to show that ..." (it isn't) and "the Einstein...
  41. H

    Landau and Lifschitz derivation question

    Greetings, On page 7 of Landau and Lifschitz Vol. 1 3rd. Ed, it says L(v'^2)=L(v^2+2\bf{v}\cdot\bf{ε}+\bf{ε}^2). They then Taylor expand in powers of ε, getting (ignoring second order terms and higher) L(v'^2)=L(v^2)+\frac{\partial L}{\partial v^2}2\bf{v}\cdot\bf{ε}. The...
  42. D

    Rutherford Scattering Derivation

    Homework Statement I'm trying to work out the derivation of the the Rutherford scattering trajectory. I understand the conservation of linear momentum, and that the only force acting is the coulomb force between the incoming particle and the target nucleus. Early on in the derivation I'm...
  43. M

    Decrease in pressure due to adiabatic expansion derivation?

    Homework Statement Show that \frac{dp}{p} =\frac{\gamma}{\gamma-1}\frac{dT}{T} if the decrease in pressure is due to an adiabatic expansion.Homework Equations Poisson equations: Pv^{\gamma} Tv^{\gamma - 1} Ideal Gas Law: Pv=R_{d}T, where R_{d} is the dry air gas constant. Hydrostatic...
  44. V

    Questions about the derivation of the gibbs entropy

    In statistical mechanics the macro-state of a system corresponds to a whole region in the microscopical phase-space of that same system, classically, that means that an infinity of micro-states relate to a single macro-state. Similarly, given a hamiltonian, a whole surface in the microscopical...
  45. C

    OLS Estimator, derivation sigmahat(beta0hat)

    Good day, in the lectures of emperical economic research of my uni, we got to the topic of Linear Regression with one regressor. There I encountered upon: {\hat{\sigma }_{\hat{\beta }_{0 }}}^{2 }=\frac{1 }{n }\cdot \frac{\text{var }{\left( {\left[ 1 -{\left( \frac{\mu _{x }}{E {\left( {X _{i...
  46. C

    Derivation of Clausius Inequality

    I have been reading about the derivation of Clausius' Inequality and there are a few things I do not understand. I have attached an image of the cycles. B) shows one carnot engine performing work ##d W_i## per cycle and delivering heat ##d Q_i## per cycle. For ##T'## to remain unchanged, it...
  47. S

    Breit-Wigner formula derivation

    Does anyone know where this forumula comes from? http://iopscience.iop.org/0067-0049/134/1/151/fulltext/ I don't quite understand the resonance widths, it's probably a naive question but what is 'resonating' in this context? Thanks!
  48. L

    Derivation of Height Function given an angle

    Hey everyone, I'm currently doing research at a University, I've been working on a problem for a few hours and wrote up a quick paper that shows my derivation of a certain height based on an angle. Basically the experiment is looking at optical properties of graphene, but for this to happen we...
  49. T

    Students t-distribution Derivation

    I have attempted a derivation of the Students t-distribution probability distribution function in the attached pdf. I defined T to be Z/sqrt(W/v) where Z has standard normal distrubution and W has chi squared distribution with v degrees of freedom. I know that Z and W need to be independent, but...
  50. tomwilliam2

    Derivation of relativistic E_kin

    In my textbook there is a derivation of relativistic kinetic energy starting from an integral of the force applied over the distance required to take the particle's speed from 0 to v. There's one stage of the derivation I don't understand on mathematical grounds, which is going from: $$E_k =...
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