Chain Definition and 939 Threads

Any proof for the CHAIN RULE ?? Can somebody please show me the proof of the chain rule?? even though i have been applying that concept since i touch differentiation but i still have doubt and question on this concept!

Homework Statement If x=yz and y=2sin(y+z), find dx/dy Homework Equations Chain rule The Attempt at a Solution From y = 2sin(y+z) we get dz/dy= (1-2cos(y+z))/(2cos(y+z)) dz/dy=((1/2)sec(y+z) - 1) dx/dy = ∂x/∂y + ∂x/∂z dz/dy = z + y ((1/2)sec(y+z) - 1) = z...

Homework Statement Let x=ts^2 -1 and y=ln(s)-t Use the chain rule for functions of two variables to determine ∂f/∂t at (s,t)=(1,1) The Attempt at a Solution y=ln(s)-t ∂f/∂t= ∂f/∂s X ∂s/∂t -1 t=x+1/s^2 ∂t/∂s= -2(x+1)/s^3 ∂s/∂t=s^3/-2(x+1) ∴ ∂f/∂t= s^2/-2(x+1)...

Scenario- I'm riding a bike up a mountain road, at a constant speed of 5 mph, at a constant grade of 11%. The bike plus me (and all gear) weighs in at 200 pounds. Based on this (and excluding frictional losses, wind, etc.) how much TOTAL pressure, in pounds is on the chain? Would it be...

I think I have a rough idea how to get there...but I'm not sure. Let's assume I'm riding a bicycle, and I'm peddling at a constant pressure (torque). This is a peddling pressure which would be the exact amount which would just lift a 50 pound weight off the ground and hold it there...

Homework Statement Here is the problem: http://dl.dropbox.com/u/64325990/MATH%20253/help.PNG The Attempt at a Solution http://dl.dropbox.com/u/64325990/Photobook/Photo%202012-05-24%209%2037%2028%20PM.jpg This seems to be wrong... Since I have fx and fy which I cannot cancel out. Why...

Homework Statement Here is the problem with the solution: http://dl.dropbox.com/u/64325990/MATH%20253/Capture.PNG What I don't understand is circled in red, how did they combine dxdy with dydx? Is it with Clairaut's theorem? If it is can someone explain how it works in this case because...

Homework Statement find the stationary distribtion of ##\left( \begin{array}{ccccc} \frac{1}{2} & \frac{1}{2} & 0 & 0 & 0 \\ \frac{1}{3} & \frac{2}{3} & 0 & 0 & 0 \\ 0 & \frac{1}{3} & \frac{2}{3} & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 \\ 0 & 0 & 0 & 1 & 0 \end{array} \right)##Homework Equations...

$${x = r \cos \theta}$$, $${y = r \sin \theta}$$, $${r^2 = x^2 + y^2}$$ and $${\theta = \tmop{ \arctan} (y / x)}$$ (with some caveats for the last formula). Suppose $${u = u (x, y)}$$. Show that $${\frac{\partial u}{\partial r} = \frac{\partial u}{\partial x} \cos \theta +...

Hi, If I have the equation y' = ax - by where y = y(t) , x= x(t) and y' = \frac{dy}{dt} then what is \frac {d}{dy} y' = \frac {d}{dy}(ax - by) ? I think it would come out to \frac {dy'}{dy} = a \frac {dx}{dt}\frac {dt}{dy} - b Is that right? In general...

Attached is the image of the desired structure, my question is based on what is pictured as (CH3)2HC- I represented this group as C3H7 which does seem like the logical equivalent, but just being safe here. Am I right? Thank you!

Its not an actual homework question just principals I am unclear on. Its in relation to a standard bicycle being driven by a rider How would I calculate the minimum torque on the back wheel? How would I calculate the maximum torque on the back wheel? How would I calculate toque on the...

#Error

Homework Statement Logistics model: Consider the birth and death chain with birth rates π(n)=a + Bn and death rates μ(n) = (S + yn)n where all four constants (a, B, S, y) are positive. In words, there is immigration at rate a, each particle gives birth at rate B and dies at rate S+yn, i.e...

Homework Statement I have vector R. I need to show the R dot dR/dt = 0 => 1/2 d/dt[R dot R] Homework Equations The Attempt at a Solution I guess I've never really applied the chain rule to dot products and its throwing me off. How does one go from R.dR/dt=0 to 1/2 d/dt[R.R] = 0. I...

Homework Statement A taxicab moves between the airport, Hotel A, and Hotel B according to a Markov chain with transition probabilities: P(airport → A) = 0.7, P(airport → B) = 0.3, P(A → airport) = 0.9, P(A → B) = 0.1, P(B → airport) = 0.8, P(B → A) = 0.2. A-If the taxicab starts...

Since Calculus has supposedly been around for a long time, when is there actual evidence of the chain rule first being used?

I'm looking at one step in my thermodynamics book and they go from pV = \nu*R*T to p*dV + V*dp = \nu * R * dT I think there's an application of the chain rule in here but I don't see exactly how it's working. Could someone show me the steps in between? Thanks!

Homework Statement I have a function z, and I need to find the derivative dz/dt "using the chain rule without substitution" Homework Equations z = x^{2}y^{3} + e^{y}\cos x x = \log(t^{2}) y = \sin(4t) The Attempt at a Solution \frac{\mathrm{d} z}{\mathrm{d} t} =...

Homework Statement Find \lambda= \{\lambda_i\} with \lambda_0 = 1 if P(X_n=i+1|X_n=i) = p, P(X_n = i-1|X_n = i) = 1 - p, i \in Z, 0<p<1 Homework Equations \lambda P = \lambda The Attempt at a Solution I used my relevant equation to write out: (1-p)\lambda_0 + P\lambda_{-2} =...

How can I efficiently calculate the amount of material decayed after a specific time in a two-step decay chain? In my specific example, I have 56Ni -> 56Co -> 56Fe. The half life of the first process is 6.1 days, the second - 77.7 days. How can I accurately calculate the amount of 56Fe that...

hi.. can someone help me out with noise in engines.. i am specifically interested in noise due to running of chain on sprockets.. it is a sort of whistling noise... which are those parameters in design of sprocket and chain which contribute in noise.. we can also talk in terms of different...

Homework Statement http://data.imagup.com/10/1146211599.jpg A,B,C and D are 4 beams ..what beam we can change it to chain and this system till stay work perfectly?

If we prepare a chain of flourine atoms: F-F-F-F-F-F-F-F-F-F-F-F-F-F-F-F-F-F-F we can construct the band structure shown. I'm using flourine as an example but my question can be generalized: What do we know about the conductivity of a material (such as this 1D chain) when the fermi level lies in...

Hi I've spent a long time trying to understand this chain rule proof but I just can't get it... I have attached 2 pictures: the second one is an intuitive chain rule proof that turns out to be bogus and the first is the correct proof. So I am trying to understand first of all what does the...

Homework Statement A Mechanics tries to remove an engine from a car by attaching a chain to it from a point directly overhead and then pulling sideways with a horizontal force F. If the engine has mass 180kg, what is the tension in the chain when it makes an angle of 15 degrees with vertical...

Homework Statement z = cos(x^2 + 3y^2) x = ucosv y=usinv find dz/dv Homework Equations The Attempt at a Solution I think I can do these fairly well, but I'm a little unsure of the "protocol" for which variables to put back in. Sometimes (in this case) I can't really put...

Homework Statement This is not really a homework question but just something that I'm confused about. I'm having trouble with understanding the movement of Markov chain. Say, if S = {0,1,2...} and 0<q<1. Let p(i,i+1)=q and p(i,i-1)=1-q. I can see how this Markov chain moves (back and forth...

What I know from the chain rule is that if y and u are differentiable with respect to x then dy/dx = (dy/du)*(du/dx) Now, why is this example doesn't work: y = x^2 u = c then we have dy/dx = (dy/du) * (du/dx) = (dy/du) * 0 = 0 doesn't equal 2x I want an answer irrelated to the chain...

Im new on the forum, so I hope you guys will have some patience with me :-) I have a question about the chain rule and partial differential equations that I can't solve, it's: Write the appropriate version of the chain rule for the derivative: ∂z/∂u if z=g(x,y), where y=f(x) and...

Homework Statement I'm trying to figure out how to take grad(f(x(t)) where x(t) is a vector. Since it's part of a physics problem, it's assumed x(t) is in 3-dimensional space. The Attempt at a Solution My guess is that grad(f(x(t)) = ((∂f/∂x)(∂x/∂x),(∂f/∂x)(∂x/∂y),(∂f/∂x)(∂x/∂z)) but...

This is another problem than I've been stuck on for a long time and I tried reading and watching videos but I only find first order partial differentiation with more than two variables or higher order partial differentiation with only two variables. (I'm not calling f a variable but I am calling...

Homework Statement Imagine a system consisting of a chain that runs over two sprockets. The chain rotates around the sprockets with a constant linear velocity (i.e. the chain is taut and rigid). The front sprocket has a radius rfront and an angular speed ωfront and the rear sprocket has a...

Homework Statement Alright, so my calc class isn't getting easier and we started doing 'work' problems, and I'm just not getting it. Here's the question: A 10ft long weighs 25l and hangs from a ceiling. Find the work done in lifting the lower end of the chain to the ceiling so that its level...

Homework Statement Given the followin[Sg decay chain- X→Y→Z Solve for Nx(t), Ny(t), Nz(t) for the case of Rx(t)=\alphat and assuming Ny(t)=Nz(t)=0 Homework Equations dNx(t)/dt = -\lambdaxNx(t) + Rx(t) dNy(t)/dt = -\lambdayNy(t) +\lambdaxNx(t) dNz(t)/dt = -\lambdazNz(t) +\lambdayNy(t) The...

I have derivative dx/dt = y(u(t)) * z(u(t)) + u(t) Now, what is dx/du ? I know the chain rule should help, but I am stuck :-(

Homework Statement Homework Equations N/A The Attempt at a Solution I'll shortly explain what my reasoning is so far, but please ignore it if it comes across too jumbled: --- Let P denote the markov matrix associated with this problem, then I think I was able to argue that the...

I'm trying to understand this one derivation but this one part keeps messing me up; theta = tan^-1 (y/x) r^2 = x^2 + y^2 d theta/ d x = y/ (x^2 + y^2) how did they get this line?

->ds/dt where s is the arc length in cartesian coordinates is ((dx/dt)^2+(dy/dt)^2)^(1/2). -> Therefore by the chain rule ds/dt = ds/dp * dp/dt, but if I substitute dx/dt=dx/dp* dp/dt and dy/dt= dy/dp* dp/dt in the formula above, I get ds/dt=ds/dp * |dp/dt|?? What is happening? ->Even by...

I think i found the solution to my problem but i was hoping to have someone check to make sure i did not make a mistake. \xi = x - ct...... (1) u(t,x) = v(t,\xi)......(2) Taking the derivative d[u(t,x) = v(t,\xi)] \frac{\partial u}{\partial t}dt + \frac{\partial u}{\partial x}dx =...

Homework Statement I am trying to solve the transport PDE using a change of variables and the chain rule, and my problem seems to be with the chain rule. The PDE is: \frac{\partial u}{\partial t}+c\frac{\partial u}{\partial x} = 0 ......(1) The change of variables (change of reference frame)...

Homework Statement Prove the chain rule for Jacobi determinants \frac{d(f,g)}{d(u,v)} * \frac{d(u,v)}{d(x,y)}=\frac{d(f,g)}{d(x,y)} Homework Equations Definition of Jacobi determinant \frac{d(f,g)}{d(u,v)} = \frac{d(f,g)}{d(u,v)} = det \begin{bmatrix} \frac{df}{du}&\frac{df}{dv} \\...

Hello, Looking through a book on calculus I found the following explanation for the chain rule and I have one unclear thing that I'd like to ask for help on. The canonical example is used, y is a function of u: y = u^{n} and u is a function of x (let's say) u = 3x - 2 therefore by composition...

Question : Let Xn be the maximum score obtained after n throws of a fair dice a) Prove that Xn is a markov chain and write down the transition matrix Im having a problem starting the transition matrix im assuming the states are meant to be the sum. then do you write out the transition...

Homework Statement z = f (x^2 + y^2) prove using multi var chain rule that y * dz/dx - x * dz/dy = 0 Homework Equations The Attempt at a Solution honestly i just need to no how to start it then I am sure i could figure the rest out so i would find dz/dx and dz/dy then...

Homework Statement Let f be a differentiable function of one variable, and let z = f(x + 2y). Show that 2∂z/∂x − ∂z/∂y = 0 Homework Equations Multi-variable chain rule The Attempt at a Solution I have no idea where to start with this, any advice would be greatly appreciated...

Hi, I need help with answering this question. Firstly, I'm not sure what the transition matrix should like. Should there be 2 states? One where both switches are off and one where both switches are on? The question is: Suppose that each of 2 switches is either on or off during the day. On...

Homework Statement I'm trying to follow my textbook on an application of the chain rule. Two objects are traveling in elliptical paths given by the following parametric equation. x1 = 4 cos t x2 = 2 sin 2t y1 = 2 sin t y2 = 3 cos 2t At what rate is the distance between the two...

Homework Statement Differentiate the functions using chain rule. 2(x3 −1)(3x2 +1)4 Homework Equations Chain Rule = f ' (g(x))g' (x) The Attempt at a Solution I don't know how to do using chain rule, but product rule is easier So using product rule, = f ' (x) g(x) + f (x)g'...

Homework Statement [12] 3.Thetemperature T(x, y) at a point of the xy-plane is given by T(x,y)= ye^(x^2). A bug travels from left to right along the curve y = x^2 at a speed of 0.01m/sec. The bug monitors T(x, y) continuously. What is the rate of change of T as the bug passes through...