Chain Definition and 939 Threads

Hello all, I am stuck on what seems like a rather simple problem: Let f:\mathbb{R}^3 \rightarrow \mathbb{R} and g:\mathbb{R}^2\rightarrow \mathbb{R} be differentiable. Let F:\mathbb{R}^2 \rightarrow \mathbb{R} be defined by the equation F(x,y)=f(x,y,g(x,y)). Find DF in terms of the...

Find the derivative of y = [x + (x + (sin(x)2))5]3 I know that power and chain rule combined uses the equation n[g(x)]n-1 * g'(x) I don't even really know where to start with so many layers in the equation. I can only find examples with only one power. with my attempt I got...

Random question: suppose in the military that a recruit is given a direct order to do something by his captain, which obviously goes against the captain's own orders. Is the recruit exempt from the punishment because he was just following his own orders? If he is not exempt from the...

I'd just like some confirmation on my answers, and I'd appreciate it if someone could take the time to explain why what I did is right. I solved it with a lot of hand-waving, so I'm very unsure of how I reached the answers. A uniform chain of weight W is strung between two vertical walls. The...

Hi everybody! I'm looking for the critical exponent ν (i.e. the one of the correlation length) of the Heisenberg (i.e. equal coupling in all directions) antiferromagnetic spin-1/2 model in 1D... Furthermore, do you know to which universality class it belongs? Is it true that it's the...

im trying to do the Euler problem #14 - to determine which starting value under one million produces the longest chain and here's my code in Python Count=[] Count2=[] List=[] def seq(n): if n%2==0: return n/2 else: return 3*n+1 m=1 for i in range(1,1000000): j=i List.append(j) while...

In fluid mechanics velocity is given in the form \textbf{V}=u\textbf{i}+v\textbf{j}+w\textbf{k} Homework Statement A two-dimensional velocity field is given by \textbf{V}=(x^2-y^2+x)\textbf{i}+(-2xy-y)\textbf{j} At (x_o,y_o) compute the accelerations a_x\text{ and }a_y I am...

Hello everyone, I was looking at the proof of chain rule as posted here: http://web.mit.edu/wwmath/calculus/differentiation/chain-proof.html" I am having trouble understanding why delta(u) tends to 0 as delta(x) tends to 0. Can someone point out to me why that is so? Many thanks, Luca

Homework Statement I'm looking at a problem from MIT's Open Courseware on radioactive chain decay, i.e. one element decays into another decays into another, finding the quantity at time t.Homework Equations The standard linear differential equation governing exponential decay.The Attempt at a...

Homework Statement x2+y2=1 I want to differentiate this equation. I know that the answer is 2x+2y*y'=0. Homework Equations The chain rule. The Attempt at a Solution I don't understand how you get 2y*y' from y2. Shouldn't it just be 2x+2y=0?

We are given two states 1,2 in an irreducible and positive recurrent Markov chain, and their stationary probabilities \pi_1 and \pi_2 respectively, try to characterise in general the probability (distribution) of the number of visits in state 2 after two consecutive visits in state 1. Any hints?

Homework Statement A horizontal uniform board of weight 125N and length 4m is supported by vertical chains at the ends. A person weighing 500N is sitting on the board. The tension in the right chain is 250N. How far from the left chain is the person sitting? Homework Equations...

Homework Statement Rat and Cat move between room 1 and 2 using different paths. Their motions are governed by their respective transition matrices: [0.9, 0.1 ; 0.2, 0.8] [0.6, 0.4 ; 0.3, 0.7] (semi colon is a new line in the matrix, like in matlab) If they are ever in the same room...

Homework Statement A chain of mass M and length L is suspended vertically with the lower end touching a scale. the chain is released and falls onto the scale. what is the reading of the chain when a length x is fallen? neglect the size of individual links Homework Equations dp = IMPULSE=F*dt...

chain velocity?? Homework Statement A chain of metal links with total mass M = 6 kg is coiled up in a tight ball on a low-rriction table. you pull on a link at one end of the chain with a constant force F = 67 N. Evntually the chain straightens out to its full length L = 0.9 m, and you keep...

Homework Statement When the synthesizer Iimaginary device is used on solar power, describe, in simplest terms, the chain of energy transformations required. As well describe the chain for the original synthesizer running on electric power. Homework Equations I'm not to familiar with...

Homework Statement Hi all. I have an expression given by V(x,y) = ay+x2y2, where a is a constant. I wish to find the time-derivative of V(x,y), and this is what I have done: \frac{dV}{dt} = a\dot y + \frac{d}{dt}x^2y^2, where the dot over y represents differentiation w.r.t. time. My...

[SOLVED] Chain On Pulley Homework Statement Given: g = 9.8m/s^2 . A uniform flexible chain whose mass is 7 kg and length is 6 m. Given: A small frictionless pulley whose circumference is negligible compared to the length of the chain. Initially the chain is hung over the pulley with nearly...

Homework Statement Homework Equations The Attempt at a Solution My dought is about if ,dw/dy*dy/dt = (-2)t^(-3)*dy/dt

Homework Statement A chain of metal links with total mass M = 6 kg is coiled up in a tight ball on a low-friction table. You pull on a link at one end of the chain with a constant force F = 69 N. Eventually the chain straightens out to its full length L = 1.0 m, and you keep pulling until...

speed of chain?? Homework Statement A chain of metal links with total mass M = 6 kg is coiled up in a tight ball on a low-friction table. You pull on a link at one end of the chain with a constant force F = 69 N. Eventually the chain straightens out to its full length L = 1.0 m, and you...

Homework Statement You have a new job designing rides for an amusement park. In one ride, the rider's chair is attached by a 9.0-m-long chain to the top of a tall rotating tower. The tower spins the chair and rider around at the rate of 1 rev every 4.0 s. In your design, you've assumed that...

Hi, I'm new to these forums so not exactly sure where to place this question, although calculus seems a good bet, so here goes: I'm currently taking a mechanics course at my university (current subject is work/energy), and I'll just post this snippit from our textbook (Physics for Scientists...

Homework Statement Differentiate y = \left(\frac{x+2}{\sqrt[3]{x}}\right)3 Homework Equations -Chain Rule -Quotient Rule -Power Rule -Product Rule? The Attempt at a Solution First I got rid of the fraction by taking the negative of x^3, and then used the chain rule to differentiate...

Homework Statement First problem: Let f(x,y) = x-y and u = vi+wj. In which direction does the function decrease and increase the most? And what u (all of them) satisfies Duf = 0 Second problem: Let z = f(x,y), where x = 2s+3t and y = 3s-2t. Determine \partial{z^2}/\partial{s^2}...

Homework Statement A 800 kg boulder is raised from a quarry 150 m deep by a long uniform chain having a mass of 580 kg. This chain is of uniform strength, but at any point it can support a maximum tension no greater than 2.90 times its weight without breaking. What is the maximum acceleration...

Homework Statement It is given that, \left(e^{-t^2}y\right)'=e^{-t^2}\left(y'-2ty\right), which I am trying to work out. Homework Equations f'(t)=h'(g(t))g'(t) (u\cdot v)'=u'v+uv'The Attempt at a Solution f(t)=e^{-t^2}y=h(g(t)) \text{let}\;g(t)=u=t^2\;\text{and}\;h(u)=e^{-u}y...

Hello! I got one question for you. How come that (f \circ g)'(x) = f'(g(x)) g'(x) ? Since (f \circ g)'(x)=f(g(x))' , f'(g(x))=f'(g(x)) g'(x). And now we can rewrite the equation like 1=g'(x) I don't understand that part. Also I don't understand why the flawed proof of the chain rule...

Homework Statement A chain of length L and total mass M is released from rest with its lower end just touching the top of a table. Find the force exerted by the table on the chain after the chain has fallen through a distance x. (Assume each link comes to rest the instant it reaches the...

Hello. Let g(x,y) be a function that has second order partial derivatives. Transform the differential equation \frac{\delta ^{2}g}{\delta x^{2}}-\frac{\delta ^{2}g}{\delta y^{2}}=xyg by chaning to the new variables u=x^2-y^2 and v=xy The equation doesn't have to be solved. Okay, so this is...

Hi I want't your help to learn about chain selection I have an electric motor of 11 kw and a gearbox I want to find a suitable chain can you help me?

Homework Statement Z is defined implicitly as a function of x,y by equation (z^2)x + 3xy^2 + e^((y^2)z) = 4. Find dz/dx Homework Equations dz/dx = -Fx/FzThe Attempt at a Solution Fx= z^2 + 3y^2 Fz=2zx+(y^2)e^((y^2)z) dz/dx= (z^2+3y^2)/[2zx+(y^2)e^((y^2)z)] I'm not sure if I used the partial...

Do Uranium-235 nuclei ever undergo fission spontaneously? If not how does a nuclear bomb actually work? I understand that two pieces of Uranium (which are subcritical) are driven togther by a chemical explosion and this initiates the chain reaction; however, if nuclei can not undergo fission...

Hi all, I'm wanting to write a small program simulating a 1D lattice with some motion. I have the equation: m_{n}\frac{d^{2}u_{n}}{dt^{2}}= k_{n,n+1}(u_{n+1}-u_{n})+k_{n-1,n}(u_{n-1}-u_{n}) Then using a simple trial plane wave (u_{n}=Ae^{-i\omega t}). It boils down to: - \omega^{2}...

This is stuff I do in order to understand analytical mechanics better, I encounter the followin thing: \frac{\partial L}{\partial \dot{\phi}} = \text{?} Where \dot{\phi} = \frac{\partial \phi}{\partial q} \frac{dq}{dt} = \frac{\partial \phi}{\partial q} \dot{q} I should know this! It is...

Trek recently released a belt driven bicycle (instead of chain drive) which led to a discussion among some cycling friends. Which led to discussion of torque, power output, etc. Anyway, I'm trying to compare the chain tension of a motorcycle vs the chain tension of a bicycle. I'm better with...

Homework Statement i have a scenario which i have to find the proportion of time spent in each area by a person using markov chains. i was given a word problem, which i have put into a matrix and the question asks what the proportion of time is spent in each area A, B and C. Homework...

Sorry if the title is a bit blunt, but it's basically like this. There's this machine I'm working with. It's kinda using Gear + Chain to drive the output. Initially, they were all driven by gears but the gear is spoil every 2 months. So then it was changed to chain instead but now the...

Homework Statement 2x^2+5xy-y^2=1 Homework Equations d/dx(f(u)x))=df/du * du/dx The Attempt at a Solution i got (2y-4x)/5x but I'm almost certain that its wrong...can anyone help me?

Homework Statement A chain lies on a frictionless table at rest, half off the edge, and half on. As soon as it is let go, it begins accelerating due to gravity only. Determine the acceleration of the chain as a function of time. The mass is m, gravity is g, and the length of the chain is L...

Homework Statement f(x)= x^2(x-2)^4 solve for f '(x) Homework Equations f(x) = x^2(x-2)^4 The Attempt at a Solution 4x^2(x-2)^3 The answer is given in the book as 2x(x-2)^3(3x-2) i'm not following any progression that gets me to that solution regardless of how many times I...

Hi all, I am supposed to calculate the energy of chain of spins where the magnetic field H = 0. For the first chain the spins are all aligned in the same direction - up - hence the energy U = -NJ where N is the total number of spins. Next, the half the chain is spin up and the other...

Chain rule difficulties, due tomorrow! Homework Statement Find the derivative of y=e^square root of 1+tan(sinx) Homework Equations chain rule: F'(x)=f'(g(x)) * g'(x)The Attempt at a Solution I thought I had it and then while I was looking at other chain rules and started doubting my...

Homework Statement You have a new job designing rides for an amusement park. In one ride, the rider's chair is attached by a 9.0-m-long chain to the top of a tall rotating tower. The tower spins the chair and rider around at the rate of 1 rev every 4.0 s. In your design, you've assumed that...

Homework Statement You have a chain of length 10m with 80kg, how much work does it take to lift this chain from one end to 6ft? Homework Equations \delta = \frac{10}{80} = .125 The Attempt at a Solution W = \int{F(x)}\,dx = \int^{6}_{0}{\delta lg}\,dl = \frac{\delta l^2g}{2}...

Homework Statement A chain hangs verticaly from a building. The chain is 30 ft long and is 5 lb/ft3, how much work is needed ot lift the bottom of the chain to the top.Homework Equations If you put the axis where the chain is hanging your limits would be 0 and -30The Attempt at a Solution So I...

Hi! I'm studying for an exam on Friday, and I'm stuck on this problem: A uniform chain of length 8.00m initially lies stretched out on a horizontal table. A. Assuming the coefficient of static friction between chain and table is 0.600, show that the chain will begin to slide off the table if...

Chain Rule Question is Find the derivative of F(x)= 3 sq rt of x^3-1 First step I did was changing the Sq RT to (x^3-1)^3/2 Then I solved it by 3/2(X^3-1)^1/2*3X^2 Another problem very similar F(X)= 3 SQ RT of X^4+3x+2 Step 1 (X^4+3x+2)^3/2 Then 3/2(X^4+3x+2)*4x^3+3 I know how...

Homework Statement Find the derivative: ( (X^3-1)/(X^3+1) )^1/3 Homework Equations d/dx f(g(x)) = f'(g(x)) * g'(x) quotient rule x/a x'a-xa'/a^2 The Attempt at a Solution first i used the chain rule and quotient rule to get 1/3 ((x^3-1)/(x^3+1))^-2/3 * ((3x^2(x^3+1) -...

Homework Statement derivative of esec(x) The Attempt at a Solutionu = sec(x) y = eu du/dx = tan(x)sec(x) dy/du = eu dy/dx = dy/du * du/dx = esec(x)tan(x)sec(x)