Chain Definition and 939 Threads

Homework Statement here's the question, is my concept correct? the ans is 9.86 cm, but my ans is 13 cm, can anyone tell me which part is wrong? Homework Equations The Attempt at a Solution

Homework Statement If possible, please check my work for any large errors. y = 10kl - √k - √l k = (t/5) + 5 l = 5e^t/10 Evaluate at t = 0 using chain rule. Homework Equations y = 10kl - √k - √l k = (t/5) + 5 l = 5e^t/10 The Attempt at a Solution = ∂y/∂k * dk/dt + ∂y/∂l * dl/dt = (10l -...

Homework Statement I am confused because for each problem there is no equation and for one no intermediate variables. Compute dy/dt when a) y = f(t, t^2, t^3) b) y = g(t, h(t), k(t^2)) Homework Equations a) y = f(t, t^2, t^3) b) y = g(t, h(t), k(t^2)) The Attempt at a...

Hello all, I need some help with this chain rule problem. \[F(x,y)=f\left (\frac{x-y}{x+y} \right )\] It is known that: f'(1)=20,f'(2)=30, f'(3)=40 and \[f''(1)=5,f''(2)=6,f''(3))=7\]Find \frac{\partial F}{\partial x}(2,-1) and \[\frac{\partial^2 F}{\partial x\partial y}\]The final...

is there any way to add power of two independent chain drives having different rpm , such that slipping doesn't occur and driven shaft move with the added resultant power

Energy Question -- Chain sliding off frictionless table Homework Statement Here is the problem that's confusing me: A frictionless chain of length 2.00m is held with 20.0% of its length hanging over the edge of a table. The chain is then released. Determine its speed the moment the entire...

I have no idea how to solve this. All i can think of is that you need mass to solve the problem. Homework Statement A chain is lying flat on a table. It has no friction against the flat surface. You pull the chain to the edge of the table so that it from a resting state starts to slide down...

I'm randomly having trouble applying the chain rule to functions (well, 1 function in particular), I was hoping someone could quickly walk me through this simple problem as I don't know where I've gone wrong. I've tried U substitution, chain/product rule, factoring answer...but I just can't see...

Differentiate the following by rule y=(2x2+4x)5 Is the chain rule the right rule to use? dy/dx=dy/du*du/dx Let U=2x2+4x du/dx=4x+4 y=(u)5 → dy/du=5(u)4 dy/dx=5(u)4*4x+4 dy/dx=5(2x2+4x)4*4x+4 dy/dx= 30(2x2+4x)44x dy/dx= 30(2x216x)4 I'm wondering if I am on the right...

Dear all, I was wondering how the radii of curvature can be calculated of a flexible chain (polymer chain). I have the x,y and z values of the polymer chain. For a 2D chain, I can calculate the curvature radii (http://www.intmath.com/applications-differentiation/8-radius-curvature.php). I am...

Homework Statement A chain with length ℓ is held stretched out on a frictionless horizontal table, with a length y0 hanging down through a hole in the table. The chain is released. As a function of time, find the length that hangs down through the hole (don't bother with t after the chain...

Homework Statement A chain is wrapped around a disk of radius R. The tension of chain is T. What is the coefficient of friction, if when the disk is spinning at angular velocity ω, the chain slips down? See image attached. Homework Equations II Newton law a_{centripetal} =...

Let $z:\mathbb{R}^2\to \mathbb{R}$ an function of kind $C^2(\mathbb{R}^2)$. What transforms the equation $2\dfrac{\partial^2 z}{\partial x^2}+\dfrac{\partial^2 z}{\partial x\partial y}-\dfrac{\partial^2 z}{\partial y^2}+\dfrac{\partial z}{\partial x}+\dfrac{\partial z}{\partial y}=0$ under the...

Hello, I need to do this proof here: I tried but didn't get what I wanted, so I was re-thinking the whole thing. If I say u=y+ax and v=y-ax, should I do something like (dz/df)*(df/du)*(du/dx)+...? Because I tried just with u and v (without f and g), and I got almost what I wanted, with a...

For example, if you differentiate 6*sqrt(x^5), would you use the chain rule? If not, why? Thank you!

Hello all, I have a problem with second derivatives and chain rule. I am working on the question attached (sorry, my Latex editor wasn't working...) I need to find F'(1) and F''(1). I managed to solve F'(1), but I can't figure out F''(1). In the second image attached, you can see the solution...

Homework Statement Homework Equations The Attempt at a Solution I am not sure how to proceed with the given problem. I can write down the net force on any of the charges but what should be the condition that the chain breaks? :confused: Any help is appreciated. Thanks!

Hello everyone, I am reading a proof of the chain rule given in this link: http://kruel.co/math/chainrule.pdf Here is the portion I am troubled with: "We know use these equations to rewrite f(g(x+h)). In particular, use the first equation to obtain f(g(x+h)) = f(g(x) + [g'(x) + v]h)...

Hi fi you look at quesiotn 16b in the following link they try to find dE/dx. they use the chain rule. the chain rule says dF/dt=dx/dt*dF/dx+dy/dt*dF/dy if F=f(x,y) and x=f(t) and y=f(t). But in 16b they're trying to find dE/dx and as part of the use of the chain rule they try to find...

Hi, I’m a bit confused. I am familiar with the chain rule: if y=f(g(t,x),h(t,x)) then dy/dt=dy/dg*dg/dt+dy/dh*dh/dt To show that an equation is invariant under a galiliean transform, it’s partially necessary to show that the equation takes the same form both for x and for x’=x-v(T). So if you...

Hey! :o Given the Markov chain $\{X_n, n \geq 1\}$ and the following probability transition matrix: $\begin{pmatrix} 0 & 1/3 & 2/3\\ 1/4 & 3/4 & 0\\ 2/5 & 0 & 3/5 \end{pmatrix}$ All states communicate, so the chain is irreducible, isn't? Could you tell me if the state $2$ is periodic?

Hello everyone, first post here. Homework Statement Let f(x,y)=x2y+y2x , where x=sin2t and y=cos2t. Use the chain rule to compute df/dt Homework Equations f(x,y)=x2y+y2x x=sin2t y=cos2t The Attempt at a Solution This is pretty much the exact wording of the question...

I'm not entirely sure if this belongs in homework or elsewhere -- I'm self-teaching working through a basic calculus text, so it's not homework per se. In any case it's a simple differentiation problem wherein I am supposed to differentiate: f(x) = x(3x-9)^3 f'(x) = 3x(3)(3x-9)^2 Applying...

How do I compute the following differentiation by chain rule? \frac{d}{d\lambda}(\lambda^{-1}\phi(\lambda^{-1}x)) It is not a homework, but I can't figure out the exact way of getting the answer -\phi(x)-x^{s}\partial_{s}\phi(x)

Homework Statement You are lifting a chain straight up at a constant velocity v_0. The chain has a linear mass density λ. What is the force required to lift the chain as a function of height? The Attempt at a Solution U = mgh = λygh The height in the potential energy is the same as...

Homework Statement One end of the chain falls through a hole in its support and pulls the remaining links after it in a steady flow. If the links which are initially at rest, acquire the velocity of the chain suddenly and without frictional resistance or interference from the support or from...

Homework Statement We have a chain of 10 blocks, all of them joined by a thin rope and placed in a straight line. Suddenly, other two blocks collide with v speed at one end with the chain of the 10 blocks. It is assumed that the table is frictionless and the collision is elastic. The main...

Homework Statement Let h(u,v) = f(a(u,v), b(u,v)), where a_u = b_v and a_v = -b_u. Show that h_{uu} + h_{vv} = (f_{xx} + f_{yy}) (a^2_u + a^2_v). Homework Equations The Attempt at a Solution I suppose my first question is where the x's and y's come from. (I thought at first it...

Homework Statement Show that any function of the form ##z = f(x + at) + g(x - at)## is a solution to the wave equation ##\frac {\partial^2 z} {\partial t^2} = a^2 \frac {\partial^2 z} {\partial x^2}## [Hint: Let u = x + at, v = x - at] 2. The attempt at a solution My problem with this is...

Take \(U(\eta) = u(x - ct)\) and the wave equation \(u_{tt} - u_{xx} = \sin(u)\). Then making the transformation, we have \[ (1 - c^2)U_{\eta\eta} = \sin(u). \] My question is the chain rule on the differential. \[ U_{\eta} = \frac{\partial u}{\partial x} \frac{\partial x}{\partial\eta} +...

Homework Statement Find the second derivative of $$9x^2+y^2=9$$ Homework Equations Chain rule The Attempt at a Solution I find the first derivative first. $$18x+2y\frac{dy}{dx}=0$$ $$\frac{dy}{dx}=-9\frac{x}{y}$$ I then find the second derivative...

Homework Statement Find the derivative of $$y=cos(\frac{1-e^{2x}}{1+e^{2x}})$$ Homework Equations Chain rule The Attempt at a Solution $$y=cosu$$ $$\frac{dy}{du}=-sinu$$ $$u=\frac{1-e^{2x}}{1+e^{2x}}$$ $$ \frac{du}{dx}=(1-e^{2x})(-(1+e^{2x})^{-2})+(1+e^{2x})^{-1}(-2e^{2x})$$...

Homework Statement Find the derivative of [SIZE="3"]y=cos(a3+x3) Homework Equations Chain rule The Attempt at a Solution y=cosu [SIZE="3"] \frac{dy}{du} = [SIZE="3"]-sinu [SIZE="3"]u=[SIZE="3"]a3+x3 [SIZE="3"] \frac{du}{dx} = [SIZE="3"]3a2+3x2 [SIZE="3"]\frac{dy}{dx}...

Homework Statement Find the derivative of y=xe-kx Homework Equations Chain rule The Attempt at a Solution y = xeu \frac{dy}{du} = xeu+eu u = -kx \frac{du}{dx} = -k \frac{dy}{dx} = (xe-kx+e-kx)(-k) = e-kx(x+1)(-k) = e-kx(-kx-k) The answer is e-kx(-kx+1)...

1. Find the derivative of y=e\sqrt{x} Homework Equations Chain rule The Attempt at a Solution y=[SIZE="3"]eu [SIZE="3"] \frac{dy}{du}= [SIZE="3"]ueu-1 u=[SIZE="3"]\sqrt{x} [SIZE="3"]\frac{du}{dx}= [SIZE="3"]\frac{1}{2}x-1/2 [SIZE="3"]\frac{dy}{dx}=...

Hi, I have a test prep question regarding Chain Rule, please see the problem and my attempt below. I believe part A is okay but part B, I'm just confused, seems like there is a part missing from the question, or at least how I'm use to doing it. Homework Statement A. Let f(x, y) =...

If ##r## is a function of ## x,y##, then \delta r= \frac{\partial r}{\partial x}\delta x + \frac{\partial r}{\partial y}\delta y Means Small change of r = ##\left[\frac{\partial r}{\partial x}\right]_{y=k}## X (Small change of x) + ##\left[\frac{\partial r}{\partial y}\right]_{x=k}## X...

Homework Statement Solve d^2x/dt^2 = (3x^3)/2 when dx/dt = -8 and x = 4 when t = 0 2. The attempt at a solution v = dx/dt dv/dx = d^2/dx^2 d^2x/dt^2 = v(dv/dx) = (3x^3)/2 v dv = (3x^3)/2 dx integrating and using limits and you get : v^2/2 -32 = (3x^4)/8 - 96 ...

Homework Statement A chain of three links, each with a mass 0.2 kg, is being pulled up by a person lifting the top link with 8.88 N of force and the chain accelerates upward. Calculate three forces that are acting on the middle link while the chain is accelerating. Homework Equations ƩF = ma...

Homework Statement Solve (d^2x)/(dt^2) = 2x(9 + x^2) given that dx/dt = 9 when x = 0 and x = 3 when t = 0 Homework Equations The Attempt at a Solution v = dx/dt ...... dv/dx = d^2x/dt^2 dv/dx = v(dv/dx) v(dv/dx) = 18x +2x^3 integrating and evaluating using...

Homework Statement We are deriving the PDE that models a hanging chain of Length L. The x-axis is placed vertically. Positive direction points upwards. The fixed end of the chain is at x=L. Let u(x,t) denote the deflection of the chain. We assume the deflection is in the x,u plane. Let...

[b]1. Ashcroft and Mermin 22.1 Reexamine the theory of the linear chain without making the assumption that only nearest neighbors interact, using the harmonic potential energy of the form: U^harm=∑_n▒∑_(m>0)▒1/2 K_m [u(na)-u([n+m]a) ]^(1/2) Show that the dispersion relation must be...

could someone show me how \frac{∂}{∂t}(\frac{∂z}{∂u})= \frac{∂^2z}{∂u^2} \frac{∂u}{∂t} where z=z(u) u=x+at

Homework Statement The atoms having in each case, the mass m and are located at positions with x i i ∈ Z. The rest position of the ith atom is i · a where a is the lattice constant of the crystal. The interaction between the atoms can be modeled in a simple approximation, as a spring force of...

It seems to me to follow from the definition of a partial derivative. If f(x,y) = fx + fy, then what else can Δf be other than ∂f/∂x*Δx + ∂f/∂y*Δy? Then in the limiting case, the changes in f, x and y becomes differentials instead. All this seems to be given by the definitions themselves, is...

mechanical design -- cam timing chain versus gear-driven hey all, I am a mech-e student, but I am still in the infancy of my degree, so I haven't really had any courses pertaining to this sort of thing, but having work with cars for a number of years, and having what I consider a strong...

Hi! I do not understand the math used in the beginning of this video: In example 1 (4 minutes in the video), why is it wrong to simply solve the problem like this: \vec{V} = [x,-y] \Rightarrow \frac{d\vec{V}}{dt} = [\frac{dx}{dt},-\frac{dy}{dt}] = \vec{a} = [V_x,-V_y], where V_x and V_y are...

Is \frac{∂y}{∂x}×\frac{∂x}{∂z}=-\frac{∂y}{∂z}?

Homework Statement Consider the following (simple) epidemic model: A population of size N consists of infected and susceptible individuals. During each time period, each of the N choose 2 possible pairs in the population will come in contact with probability p. If a pair is in contact and...

Homework Statement A chain AB of length ##l## is located in a smooth horizontal tube so that its fraction of length ##h## hangs freely and touches the surface of the table with its end B. At a certain moment, the end A of the chain is set free. With what velocity will this end of the chain slip...