Derivative Definition and 1000 Threads

For the derivative: dy/dt = ry ln(K/y) I am trying to solve the second derivative. It seems like an easy solution, and I did: d^2y/dt^2 = rln(K/y)y' + ry(y/K) which simplifies to: d^2y/dt^2 = (ry')[ln(K/y) + 1/Kln(K/y) Unfortunately, the answer is d^2y/dt^2 (ry')[ln(K/y) - 1] and I don't...

Find the optimum frame length nf that maximizes transmission efficiency for a channel with random bit erros by taking the derivative and setting it to zero for the following protocols: (a) Stop-and-Wait ARQ (b) Go-Back-N ARQ (c) Selective Repeat ARQ My work has been uploaded I am a bit rusty on...

Homework Statement i need to show that the peak of the maxwell Boltzmann distribution is equal to 1/2 kt. Homework Equations maxwell Boltzmann distribution according to modern physics 3rd edition by kenneth kramer. ill try to do my best with this N(E)= \frac{2N}{√∏}...

Hi I need help regarding following can I write following partial derivative wrt x multiplied by Ax (∂A[x])Ax =∂(Ax^2)

Homework Statement In Griffiths, the following boundary condition is given without proof: ∂Aabove/∂n-∂Abelow/∂n=-μ0K for the change in the magnetic vector potential A across a surface with surface current density K, where n is the normal direction to the surface. A later problem asks for a...

Is rather a question of calculus skills, but how do I get the time derivative of the Hubble parameter here in [1]? Is it the Leibnitz rule, the chain rule, some clever re-arrangement? thank you

In class we were given an example where \frac{dP}{dt}=P(a-bP). We found the critical points to be P=0 and P=a/b. We wanted to know if the derivative is always positive or negative between the two critical points. The prof said you could pick an arbitrary point between the two, such as...

On the surface of a unit sphere two cars are on the equator moving north with velocity v. Their initial separation on the equator is d. I've used the equation of geodesic deviation...

Homework Statement I can't seem to figure out how this next step of this derivation for equation 2.33 was produced. This is a graduate level textbook on Adaptive Backstepping.

$$\d{}{x}\frac{1}{\sqrt{x}}$$ by the definition of the derivative. $$\lim_{{h}\to{0}}\frac{\frac{1}{\sqrt{x+h}}-\frac{1}{\sqrt{x}}}{h}=\lim_{{h}\to{0}}\frac{\sqrt{x}-\sqrt{x+h}}{h\sqrt{x^2+2xh}}=\lim_{{h}\to{0}}\frac{x-(x+h)}{h\sqrt{x^2+2xh}\left(\sqrt{x}+\sqrt{x+h}\right)}$$ Setting $h=0$...

$r(t)=\left\langle t-2, t^2+1 \right\rangle$, $t=-1$ sketch the plane curve with the given vector equation. $x=t-2$ and $y=t^2+1$ $x+2=t$ $(x+2)^2=t^2$ $(x+2)^2+1=t^2+1$ $(x+2)^2+1=y$ $x^2+4x+4+1=y$ $y=x^2+4x+5$ it's a parabola find $r'(t)$ $r'(t)=\left\langle 1, 2t \right\rangle$ sketch...

Homework Statement Find (\frac{dV}{dp})_{n,T} for the Van de Waals gas law Homework Equations Van de Waals gas law: (\frac{p+an^2}{V^2})(V-nb)=nRT The Attempt at a Solution I just started doing problems like these so I would like to know if I am doing them right... What I did was I took...

Homework Statement If f(x) = ∫sin x0 √(1+t2)dt and g(y) = ∫3y f(x)dx, find g''(pi/6)? Homework Equations FTC: F(x) = ∫f(x)dx ∫ab f(t)dt = F(b) - F(a) Chain Rule: f(x) = g(h(x)) f'(x) = g'(h(x))h'(x)The Attempt at a Solution I tried u-substition setting u = tan(x) for the first dirivative...

Hi. Assume there's a probability ##q## for a guy to take a step to the right, and ##p=1-q## to take one to the left. Then the probability to take ##n## steps to the right out of ##N## trials is ##P(n) = {{N}\choose{n} }q^n p^{N-n}##. Now, what is ##<n>##? My textbook in statistical physics...

Hello. I'm learning about Lie derivatives and one of the exercises in the book I use (Isham) is to prove that given vector fields X,Y and one-form ω identity L_X\langle \omega , Y \rangle=\langle L_X \omega, Y \rangle + \langle \omega, L_X Y \rangle holds, where LX means Lie derivative with...

can anyone tell me the difference of application of total derivative and partial derivative in physics? i still can't figure it out after searching on the internet

many books only tell the operation of total derivative and partial derivative, so i now confuse the application of these two. when doing problem, when should i use total derivative and when should i use partial derivative. such a difference is detrimental when doing Physics problem, so i...

Homework Statement Assume the notation log(a, x) implies log base a of x, where a is a constant (since I don't know LaTeX). PROBLEM: If y = [log(a, x^2)]^2, determine y'.Homework Equations Chain Rule and Logarithmic DifferentiationThe Attempt at a Solution y' = 2(log(a, x^2)) *...

To do this we should use implicit differentiation. If $\displaystyle \begin{align*} y = \arccot{(x)} \end{align*}$ then $\displaystyle \begin{align*} \cot{(y)} &= x \\ \frac{\cos{(y)}}{\sin{(y)}} &= x \\ \frac{\mathrm{d}}{\mathrm{d}x} \left[ \frac{\cos{(y)}}{\sin{(y)}} \right] &=...

In the Feynman Lectures on Physics chapter 28, Feynman explains the radiation equation $$\vec{E}=\frac{-q}{4\pi\epsilon_0 c^2}\, \frac{d^2\hat{e}_{r'}}{dt^2}$$ The fact that the transverse component varies as ##\frac{1}{r}## seems fairly obvious to me since what matters is just the angle...

I think this is a textbook-style question, if I am wrong, please redirect me to the forum section where I should have posted this. This is my first time here, so I am sorry if I am messing it up. Homework Statement We have an n-dimensional vector \vec{r} with a constant length \|\vec{r}\|=1...

Dear all, I was reading this https://sites.google.com/site/generalrelativity101/appendix-c-the-covariant-derivative-of-the-ricci-tensor, and it said that if you take the covariant derivative of a tensor with respect to a superscript, then the partial derivative term has a MINUS sign. How? The...

I'm reading through Douglas Gregory's Classical Mechanics, and at the start of chapter 6 he says that m \vec{v} \cdot \frac{d\vec{v}}{dt} = \frac{d}{dt}\left(\frac12 m \vec{v} \cdot \vec{v}\right), but I'm not sure how to get the right hand side from the left hand side. If someone could point...

Hi there, I'm kind of rusty on some stuff, so hope someone can help enlighten me. I have an expression E(r,w-w0)=F(x,y) A(z,w-w0) \exp[i\beta_0 z] I need to substitute this into the Helmholtz equation and solve using separation of variables. However, I'm getting problems simplifying it to...

Homework Statement Given f(x, y, z) = 0, find the formula for (\frac{\partial y}{\partial x})_z Homework Equations Given a function f(x, y, z), the differential of f is df = \frac{\partial f}{\partial x}dx + \frac{\partial f}{\partial y}dy + \frac{\partial f}{\partial z}dz...

Homework Statement If xs^2 + yt^2 = 1 and x^2s + y^2t = xy - 4 , find \frac{\partial x}{\partial s}, \frac{\partial x}{\partial t}, \frac{\partial y}{\partial s}, \frac{\partial y}{\partial t} , at (x, y, s, t) = (1, -3, 2, -1) Homework Equations The Attempt at a Solution I...

http://arxiv.org/pdf/physics/0511103.pdf I was wondering what people thought of this paper. Please read up to at least page 3 before responding. I find it to be pretty convincing up to page 4. Thanks for any response.

I am having difficulty calculating the following derivative { \frac{2x^2-1}{(3x^4+2)^2}} Could someone demonstrate the first step algebraically? Assuming c is the exponent on the variable expression, n is the numerator and d is the denominator, I tried...

Homework Statement Trying to figure our how to solve the following: \frac{dW}{dσ} where W(σ) = 2π\int_0^∞y(H(x,σ))x,dx Homework Equations both y and H(x,y) are continuous functions from 0 to Infinity The Attempt at a Solution Tried using the leibniz rule but it's not really...

[SIZE="4"]Definition/Summary Covariant derivative, D, is a coordinate-dependent adjustment to ordinary derivative which makes each partial derivative of each coordinate unit vector zero: D\hat{\mathbf{e}}_i/\partial x_j\ =\ 0 The adjustment is made by a linear operator known both as the...

Homework Statement Find $$\frac{\text{d}}{\text{d}x}|x|$$ Homework Equations The Attempt at a Solution I know that ##\frac{\text{d}}{\text{d}x}x=1## but it's ##|x|##. For ##x>0##, derivative is 1 and for ##x<0##, derivative is -1. :confused: And what's the derivative at ##x=0##...

Hi, so this is just a quick question about taking a derivative of an integral. Assume that I have some function of position ##A(x, y, z)##, then assume I am trying to simplify $$D_i\int{A dx_j}$$ where ##i≠j##. So, I'm taking the partial derivative of the integral of A, but the derivative and...

I just need some clarification that this is fine so I have f_{x} = -2xe^{-x^2-y^2}cos(xy) -ysin(xy)e^{-x^2-y^2} now, taking the second derivative f_{xx} = [-2xe^{-x^2-y^2}+4x^2e^{-x^2-y^2}]cos(xy) - ysin(xy)[-2xe^{-x^2-y^2}]+2xe^{-x^2-y^2}sin(xy)y-cos(xy)e^{-x2-y^2}y^2

Homework Statement r(t) = ln ti + j, t > 0 find r′ (t) and r″(t)Homework Equations none The Attempt at a Solution r'(t)= 1/t i am I on the right track? The answer in the back is r'(t)= 1/t i -1/t^2 j Please help asap this is quite urgent! Thank you!

I am doing critical points and using the second derivative test (multivariable version) Homework Statement f(x,y) = (x^2+y^2)e^{x^2-y^2} Issue I am having is with the system of equations to get the critical points from partial wrt x, wrt y The Attempt at a Solution f_{x} =...

Let's say we have a function F(\vec{r})=F(s, \phi, z). Then (correct me if I'm wrong): \frac{dF}{dx}=\frac{\partial F}{\partial s}\frac{ds}{dx}+... So then what is \frac{\partial F}{\partial x}? Is it zero because F doesn't depend explicitly on x? Is it the same as \frac{dF}{dx}=\frac{\partial...

Hi, What is the derivative of a p-fold convolution? \frac{\partial}{\partial Y(\omega) } \underbrace{Y(\omega) * \dots * Y(\omega)}_{p-\text{times}} EDIT: I have two contradicting approaches - I guess both are wrong ;-) As a simple case, take the 2-fold convolution. FIRST approach...

f(z) = sq. rt of z-1 / z+1 --- both numerator and denominator are inside the radical. I can write it as (z-1)^1/2 over (z+1)^1/2, right? If I simplify it using derivative of a quotient. Should I simplify (z-1)^1/2 and (z+1)^1/2 as whole numbers and multiply them to other terms, including...

Homework Statement Find the derivative of the function. Simplify where possible. y= arctan ( (1+x)/(1-x))^1/2 Homework Equations d/dx (arctan x) = 1/(1+x^2) The Attempt at a Solution I'm really not sure where to even begin, so any help would be greatly appreciated!

This is one of the the things I did not quite master in my calculus 1 course last semester. I understand for a function to be different on a point a. It must be defined at point a n not have any cusp or appear vertically tangent. My question is for a general function. How to I sketch it's...

Hi! I'm currently reading a book where they give the Coulomb potential, gravitational potential and harmonic potential as +Q1Q2/4∏εx -Gm1m2/x +(1/2)qx2 I think I get the signs as they are used here, but when I am trying to find the force by taking the derivative of these with respect...

Homework Statement If u(t) = σ(t) . [σ'(t) x σ''(t)], show that u'(t) = σ(t) . [σ'(t) x σ'''(t)]. Homework Equations The rules for differentiating dot products and cross products, respectively, are: d/dt f(t) . g(t) = f'(t) . g(t) + f(t) . g'(t) d/dt f(t) x g(t) = f'(t) x g(t) +...

how should i go on?

Homework Statement If V=exp [ \int^{T}_{0}s(t)dt ] Homework Equations What is dV/ds(k), where 0<k<T What does this derivative even mean?? The Attempt at a Solution write V=exp(Y) dV/ds(k) = dV/dY . dY/ds(k) =V.\int^{T}_{0}ds(t)/ds(k)dt =V because ds(t)/ds(k) = 0 for all t except...

Need to find derivative using logarithmic differentiation y = \sqrt{x(x+1)} My attempt ln y = ln \sqrt{x(x+1)} ln y = \frac{1}{2}ln x(x+1) ln y = \frac{1}{2}ln x + ln(x+1) \frac{1}{y}= (\frac{1}{2}) \frac{1}{x} + \frac{1}{x+1} \frac{1}{y}= \frac{1}{2x} + \frac{1}{x+1} \frac{dy}{dx}=...

Need to find derivative y = θ(sin(ln θ)) + cos(ln θ) My work θ(cos(ln θ))(1/θ) + sin(ln θ) + (-sin(ln θ)(1/θ)) (θcos(ln θ))/θ] + sin(ln θ) + ( (- sin(ln θ))/θ) cos(ln θ) + [θsin(ln θ) - sin(ln θ)]/ θ answer in book is 2cos(lnθ)

I can't use the template here. Find the derivative of ##a^x## I know that it will be ##In(a).a^x## Now, I watched a lecture just now. How he derived this is as follows: $$\frac{\text{d}}{\text{d}x}a^x=a^x.\lim_{\Delta x \to 0}\frac{a^{\Delta x}-1}{\Delta x}$$ (I omitted some steps). Then he...

can i use the power rule to get the derivative here? f ' (x) = 3x^2 - 2(2x^1) + 1

Let $f:[0,\infty)\to\mathbb R$ be a differentiable function such that for all $a>0$ exists a constant $M_a$ such that $|f'(t)|\le M_a$ for all $t\in[0,a]$ and $f(t)\xrightarrow[n\to\infty]{}0.$ Show that $f$ is uniformly continuous. Basically, I need to prove that $f$ is uniformly continuous...

Hello, I have two problems. I'm going through the Classical Theory of Fields by Landau/Lifshitz and in Section 32 they're deriving the energy-momentum tensor for a general field. We started with a generalized action (in 4 dimensions) and ended up with the definition of a tensor...