Derivative Definition and 1000 Threads

Homework Statement We are given that ##f(z) = u(x,y) + iv(x,y)## and that the function is differentiable at the point ##z_0 = x_0 + iy_0##. We are asked to determine the directional derivative of ##f## 1. along the line ##x=x_0##, and 2. along the line ##y=y_0##. in terms of ##u## and...

Homework Statement Show that f'(x) = k/x Homework Equations f is defined from zero to infinity f(xy) = f(x) + f(y) f'(1) = k f(1) = 0 f(x+h) = f(x) + f (1+h/x)The Attempt at a Solution [/B] I know i can write f'(x) = f'(1)/x but that's all I've got so far...

What does it mean when I have to find the second derivative of a circle at a given point? (Implicit diffing) In specifics, the equation is 9x2 +y2 =9 At the point (0,3) You don't really need the rest at all, but it was just my process. This seems to make no sense. first D'v 18x+2yy'=0 Second...

Hi, So I'm working through a bunch of problems involving gradient vectors and derivatives to try to better understand it all, and one specific thing is giving me trouble. I have a general function that defines a change in Temperature with respect to position (x,y). So for example, dT/dt would...

Have a function f(x)=4x^3-x^4 Found the x values are X -1, 0, 1, 2, 3 , 4, f(Y) -5, 0, 3, 16, 27, 0 i Need to find f^{\prime}(x) and find where it incteases and decreases??f`(x)= 3*4x^2-4x^3=4x^2(3-x) what to Next?

Homework Statement A police car is parked 50 feet away from a wall. The police car siren spins at 30 revolutions per minute. What is the velocity the light moves through the wall when the beam forms angles of: a) α= 30°, b) α=60°, and c) α=70°? This is the diagram...

Do you guys know a place where I can find a proof of the formula \frac{d^{(n)}f(z)}{dz^{n}} = \frac{n!}{2\pi i}\oint \frac{f(z)dz}{(z- z_{0})^{n+1}} Thanks

Homework Statement Find \frac{\partial f}{\partial x} if f(x,y)=\cos(\frac{x}{y}) and y=sinx Homework Equations See above The Attempt at a Solution For \frac{\partial f}{\partial x} I calculated -\frac{1}{y}\sin(\frac{x}{y}) which comes out as \frac{-\sin(\frac{x}{\sin(x)})}{sinx} and this...

Homework Statement W(t) = W(y1, y2) find the Wronskian. Equation for both y1 and y2: 81y'' + 90y' - 11y = 0 y1(0) = 1 y1'(0) = 0 Calculated y1: (1/12)e^(-11/9 t) + (11/12)e^(1/9 t) y2(0) = 0 y2'(0) = 1 Calculated y2: (-3/4)e^(-11/9 t) + (3/4)e^(1/9 t)Homework Equations W(y1, y2) = |y1 y2...

The function f: R → R is: f(x) = (tan x) / (1 + ³√x) ; for x ≥ 0, sin x ; for (-π/2) ≤ x < 0, x + (π/2) ; for x < -π/2 _ For the interval (0,∞), we are interested in f such that f(x) = (tan x) / (1 + ³√x) ; for x ≥ 0 f(x) = tan x / (1 + x¹ʹ³)            (1 + x¹ʹ³)•sec²x −...

Steps for finding the derivative of 4/sqrt{x}

##dz = \frac{\partial z}{\partial x} dx + \frac{\partial z}{\partial y} dy## I'm confused as to how the total derivative represents the total change in a function. My own interpretation, which I know is incorrect, is that ##\frac{\partial z}{\partial x} dx## represents change in the x...

Homework Statement Suppose a can, after an initial kick, moves up along a smooth hill of ice. Make a statement concerning its acceleration. A) It will travel at constant velocity with zero acceleration. B) It will have a constant acceleration up the hill, but a different constant acceleration...

I was trying to see what is the covariant derivative of a covector. I started with $$ \nabla_\mu (U_\nu V^\nu) = \partial_\mu (U_\nu V^\nu) = (\partial_\mu U\nu) V^\nu + U_\nu (\partial_\mu V^\nu) $$ since the covariant derivative of a scalar is the partial derivative of the latter. Then I...

Is the derivative of a function a differential equation? I guess it would be because it involves a derivative, right? Would the solution to the equation just be the original function? Is solving a differential equation just another way of integrating? Like with finding solutions of separable...

Let's say I have Fourier series of some function, f(t), f(t)=\frac{a0}{2}+\sum_{n=1}^{\infty}(an\cos{\frac{2n\pi t}{b-a}}+bn\sin{\frac{2n\pi t}{b-a}}), where a and b are lower and upper boundary of function, a0=\frac{2}{b-a}\int_{a}^{b}f(t)dt, an=\frac{2}{b-a}\int_{a}^{b}f(t)cos\frac{2n\pi...

Homework Statement Given the functions Q(v,w) and R(v,w) [/B] K = v(dQ/dv)r and L = v(dQ/dv)w Show that (1/v)K = (1/v)L + (dQ/dw)v (dW/dv)r I have the problem attached if for clarity of the information. Homework Equations I assume everything is given in the problem. The Attempt at...

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...

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 connection...

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