# chain

1. ### velocity acceleration problem

The van travels over the hill described by y = (-0.0015x^2 + 15) ft. If it has a constant speed of 75 ft/s, determine the x and y components of the van's velocity and acceleration when x = 50 ft. This is what I found: v_y = -0.15v_x v = \sqrt{v_x^2 + v_y^2} v_x = 74.17 ft/s \leftarrow v_y =...
2. ### Find the Derivative

I have two questions. They are almost similar. I wanna know if their derivative will be same or different. (a) If y = u^5 - 8u^2 + 2u - 1, and u = (x + 10)^(1/2), find dy/dx when x = -9. (b) If y = u^5 - 8u^2 + 2u - 1, and u = (x + 10)^(1/2), find dy/dx.
3. ### Partial derivative chain rule problem.

So far this is what I get. However my answer is not correct. Could someone please help me find out why? Thanks! $x=e^{3s}cos(5t)$ $y=e^{3s}sin(5t)$ \$\frac{\partial u}{\partial s}=\frac{\partial u}{\partial x}\frac{\partial x}{\partial s}+\frac{\partial u}{\partial y}\frac{\partial y}{\partial...
4. ### Rotman's Remarks on Modules in the Context of Chain Conditions and Compostion Series

I am reading Joseph J. Rotman's book: Advanced Modern Algebra (AMA) and I am currently focused on Section 7.1 Chain Conditions (for modules) ... I need some help in order to gain a full understanding of some remarks made in AMA on page 526 on modules in the context of chain conditions and...
5. ### Show: Markov chain transition matrix always has "one" as largest eigenvalue

I stumbled across the claim: "of the transition matrix P the largest eigenvalue is always equal to one" in "Handbook of volatility models and their applications; p. 75". I think the transition matrix has to be irreducible and aperiodic, whatever that means. I tried to prove it, but this is as...
6. ### Chain rule partial derivative

Using the chain rule, dv/dt=dv/dx*dx/dt+dv/dy*dy/dt dx/dt=-4t -> evaluate at (1,1) =-4 dv/dt=-4dv/dx+4(-2) dv/dt=-4dv/dx-8 How can I find the missing dv/dx in order to get a value for dv/dt? Thanks!
7. ### Chain rule of two functions.

I need to use the chain rule to find dw/dx w=2x^2-3xy and y=2x+3 a. Use the chain rule to find dw/dx Here is my calculation. We write the chain rule for the function: dw/dx=dw/dy*dy/dx We find the partial differentials dw/dy=-3x dy/dx=2 I put in the function (3x)*2=6x I now have a...
8. ### Partial derivative using chain rule

How can we evaluate the partial derivative at the point specified? dh/dq at (q,r) = (4,5), where h(u, v) = ue^v, u = q^3, v = qr^2? I'm not getting where to start this one?
9. ### Chain rule numerical approximation

So for the chain rule for functions we have \frac{d}{dx}f(g(x))=f'(g(x))g'(x) But given that f(10)=5,f′(10)=1,g(5)=3, and g′(5)=9, what is the approximate value of g(f(10.01))? Can't seem the see how to get this. James
10. ### Chain Rule frustration

I've been working on Larson's Early Transcendentals for the last week and a half. Up until the night before last, I was off-put by the ease with which I found myself working through the lessons. Then I reached the Chain Rule. I didn't have much trouble at first, answering the first 22 with...
11. ### Chain rule

Could someone walk me through the following problems? Find the derivative of the function. h(t)=(t+1)2/3(2t-1)3 and y=cot2(sin @) @ is supposed to be the angle symbol...don't see a way to type it.
12. ### Chain rule

Find the derivative of the function. y = x sec kx This problem is at the end of the "chain rule function". I though multiplying by x would be the outer function but nothing works out to the correct answer of y' = sec kx (kx tan kx + 1). Do I use the product rule first or instead of the chain...
13. ### Halted chain reaction

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14. ### Absorption probability in discrete time Markov chain

Q: Two players, A and B are playing the following game: They have a three-card deck marked with the numbers 1, 2, and 3 and a spinner with the numbers 1, 2, and 3 on it. The game begins by dealing the cards out so that the dealer gets one card and the other person gets two. A move in the game...
15. ### Chain Rule problem (need to simplify it I think, but don't know how to proceed)

Find derivative of f(x)=2x^7(2x^5+1)^.5 So I get: d/dx= 14x^6(2x^5+1)^.5 + 2x^7(2x^5+1)^-.5 (5x^4) .....and that's all I got. plz help.
16. ### Chain rule

I don't get how they got the answer that i circled in red ink. Please refer to the image.
17. ### using the chain rule

Not sure what order to do this chain rule. I showed my work maybe that'll show you where i went wrong. I tried factoring out some stuff as the last step, maybe that's where I went wrong. My answer is boxed. Refer to the image please. Thanks!
18. ### Vector Calculus - Chain Rule Special Case

Given g(x,y,z) = (x sin(y)ez^2, ln(x)tan(2y)/z) and f(u,v) = (uv, v/u), calculate Df(g(e,pi/2,1)) using the chain rule. I tried using the formula: D(f(g(x)) = Df(y)Dg(x), but I ended up with matrices that couldn't be multiplied together. Now I'm thinking this is a special case of the chain rule...
19. ### Vector Calculus - Chain Rule

Let g be a function of one variable and let f: R2 -> R. Define h(x,y) = g(f(x,y)). When is grad(h) parallel to grad(f)? I feel like this problem isn't that difficult, but I'm honestly just not sure what it's asking me to do.
20. ### Chain Rule derivatives

Hi all. I have (x^3+4)^5 all over (1-2x^2)^3. Y'= 5(x^3+4)^4 times(3x^2) times (1-2x^2)^3 minus 3(1-2x^2)^ times (-4x)(x^3+4)^5 all over ((1-2x^2)^3)^2. I think my derivative is correct. I am not even sure on where to begin with simplifying this. This is what I have so far...