Chain rule Definition and 505 Threads

i am having trouble with this one problem. maybe you can tell me where i am going wrong. find h'(t) if h(t)=(t^6-1)^5(t^5+1)^6 so i am using product rule and to find the derivatives of each expression i am using chain rule... so i get h'(t)=30t^4(t^6-1)^4(t^5+1)^6+30^4(t^5+1)^5(t^6-1)^5...

A boat leaves dock at 2:00 PM, heading west at 15 km/h. Another boat heads south at 12 km/h and reaches the same dock at 3:00 PM. When were the boats closest to each other? I've solved other problems similar to this one, but I can't seem to figure this one out. I'm not sure what I have to do...

please help me with this assignment question. Q: gasoline is pumped from the tank of a tanker truck at a rate of 20L/s. if the tank is a cylinder 2.5 m in diameter and 15 m long, at what rate is the level of gasoline falling when the gasoline in the tank is 0.5m deep? express in exact answer...

Homework Statement The question is: How would you explain the chain rule to a classmate? My teacher wants: 1.a graph, 2. in words, 3. using math Homework Equations The Attempt at a Solution I said: for the function y=f[g(x)], the chain rule is d/dx[g(x)]. Whats the graph like?

Given: h=f\circ g , g(2)=5, g\prime(2)=3, and f\prime(5)=-2 Determine h\prime(2)

Hi, I'm struggling to understand how to find the derivative of something like this... [(2x - 1)^2] / [(x - 2)^3] The answer in my book says it is supposed to be [-(2x - 1)(2x + 5)] / [(x - 2)^4] How do I use the chain rule with the quotient rule at the same time? I even multiplied...

This is a stupid question but... The regular multivariable chain rule is: u_x = u_v v_x + u_w w_x and u_y = u_v v_y + u_w w_y where u(v(x, y), w(x, y)) Now, are there formulae for the second partials u_{xx}, u_{xy}, u_{yy} I just want to check myself (this isn't a homework problem, though...

f(t) = (1+tan t)^(1/3) differentiate using chain rule. u = 1 + tan t y = u^(1/3) dy/dt = dy/du x du/dt u=1+tan t 1/3 u^(-2/3) when u = 1 + tan t x sec^(2)t = = sec^(2)t/3(1+tan t)^(2/3) Did I do this correct??

Using the "Chain Rule" Alright I've been working on some more practice problems and doing fairly well in finding the correct derivative, until I came to this question: y = [PLAIN]http://upload.wikimedia.org/math/1/6/0/160a5b4ac79375bd4c5e13c0f3a95f73.pngcos(sin^2x)[/URL] (everything is...

I think I've got this, but I'm not quite sure, especially about multiplying to get du to be what I want. Can someone please tell me if this is correct? (The first line is the problem.) Thanks! \int\frac{3xdx}{\sqrt[3]{2x^2+3}} I set u=2x^2+3, du=4x so the problem becomes \int...

Problem: u(x) = u_1(x)u_2(x)\cdot\cdot\cdot u_n(x) Show that u'(x) = u(x)\left[\frac{u'_1(x)}{u_1(x)} + \frac{u'_2(x)}{u_2(x)} + ... + \frac{u'_n(x)}{u_n(x)}\right] Hint: Take the logarithm of u(x) first. I solved this by using the chain rule. Regarding the hint, am I missing...

ok firstly i understand how the chain rule works however I am given this table x f '(x) g(x) g'(x) h'(x) 0 7 2 ___ 32 2 8 0 -3 ___ im told to fill in the blanks where h(x)=f(g(x^2-x)) this problem has become an annoyance at first i assumed to solve i would take...

I need help solving this problem. It is in my textbook but no answer is provided in the appendix. If y=2t+3 and x=t^{2}-t, find \frac{dy}{dx} In theory this should be fairly straight forward! Simply find \frac{dy}{dt} and \frac{dt}{dx} and multiply both derivatives together to find...

I need help differentiating y=\sqrt{x-2}\sqrt{x+1} I am using a mix of the chain rule and product rule which my textbook for school wants me to use for this. So suggestions for different ways of approaching it won't help :P Anyways, thanks in advance for looking over it. It's my first...

hey how would i find the derivative of y= -18 \sin 80 t? thanks pavadrin

f(t) = 6e^{0.013t} How do I find the derivative of this? I'm confused. Do I have to use the chain rule here or the product rule, or both?

Differentiate the function: f(u) = e1/u So, I used the chain rule and figured out that f '(u) = (-u-2) e1/u My question is, why do you have to use the chain rule? I know that if f(x) = ex then f '(x) = ex Why can't I pretend that 1/u is x and then say that f '(x) = ex = e1/u In...

Question: Let Q = \sqrt{x^2 + y}e^t where (for t > or = 0) x = \sqrt{1 - e^{-2t}} and y = 2 - e^{-2t} Using the chain rule calculate dQ/dt, expressing your answer in as simple a form as possible. My work so far Subbing in values of x and y: Q = \sqrt{1 - e^{-2t} + 2 - e^{-2t}}e^t =...

I need to show that two equations equal one another. It's too complicated to display fully on here but I'm stuck on a step: dF/dr = df/dx cos2(h) + df/dy sin(h) (dF/dr)^2 = (df/dx)^2 cos^2(h) + (df/dy)^2 sin^2(h) Does anybody know how to get rid of the cos squared and sin squared...

f '(8)=5 g '(8)=3 f(4)=8 g(4)=10 g(4)=10 g(8)=2 f(8)=5 find (g o f)'(4) how do I go about setting up these types of problem.

Hi, I would like some help verifying the nature of a stationary point of the following function of two variables. f\left( {x,y} \right) = \sin \left( x \right) + \sin \left( y \right) + \sin \left( {x + y} \right) Ok so I equated grad(f) to zero and solved for x and y. I got three...

Hi, does anyone know of any websites which have some theory and perhaps some examples of the matrix version of the chain rule. Neither of the books I have covers this particular topic so I'd like to read up on it. Any help would be appreciated thanks.

Hi, I'm having trouble understanding the solution to a question from my book. I think it's got something to do with the chain rule. The problem is to prove the change of variables formula for a double integral for the case f(x,y) = 1 using Green's theorem. \int\limits_{}^{} {\int\limits_R^{}...

Hi, here is what I'm trying to do: Find \frac{\partial}{\partial x} f(2x, 3y) First of all, I'm confused by the f(2x, 3y) How does the function look like? I imagine that it is for example f(x,y) = cos(xy) - sin(3xy^2} and that therefore f(2x, 3y) = cos(6xy) - sin(54xy^2) I'm...

I'm a little confused as to when to stop taking the derivative of the inside function when using the chain rule... Lets say I have f( g(x^2) ) Would this be correct? f`( g(x^2) ) * g`(x^2) * 2x ? Or do I keep on going until the x is completely gone from the equation?

I've been having some trouble grasping the conditions necessary to apply the chain rule to achieve the derivative of an algebraic expression or even apply it to a real world situation. So, my question to those skilled in qualitatively explaining the conditions for applying the Chain Rule and...

I'm so confused. I have to find the derivative of f(x) = x^5(4^(x^2)). All of the powers are messing me up. Any help would be much appreciated. Thanks!

I have the function: y=\sqrt{x+\sqrt{x+\sqrt{x}}} I need to find separate, smaller functions which will result in the composition of this function. I tried but all I ended up with was: f(x)=\sqrt{x} g(x)=x+\sqrt{x+\sqrt{x}} Therefore, y=f(g(x)) However, this is obviously a...

Hey, I am a bit confused oh how to use the chain rule when i have 2 variables in an equation... Example : f(x,y) = (Squareroot(x)).(cosh(x+y^2)) x(s,t)=st y(s,t)=s/t When i have 2 variables, I am not sure how to split it up and use the chain rule, all the examples i found only have 1...

Hello everyone... I'm very confused... i'm suppose to find dz/dt and dw/dt but for some of the questions there is no w variable! so what do u put for dw/dt?! Also i have the following: w = xy + yz^2; x = e^t; y = e^t*sint; z = e^t*cost; so I'm trying to find dz/dt and dw/dt; dz/dt =...

h = 3x^2.y^3 find dh/dt, if x=1, and y=2 Also, dx/dt = 0.2, dy/dt = 0.1 Any ideas where i should start in order to get this out? Thanx

I'm thoroughly confused as to how and work this problem. I thought I had an ok understanding of the chain rule when I started the section's homework, but this question has me ready to gorge out my eyeballs! The Problem: --------------- Find:dy/dx at x = 2 Given: y = (s+3)^2, s = sqrt(t-3)...

chain rule agian - check my work please w = -xy-5yz+3xz, x = st, y = exp(st), z = t^2 dw/ds(5,-2) = ________________________ here's what i did: dw/ds = dw/dx*dx/ds + dw/dy*dy/ds + dw/dz*dz/ds dw/ds = (3z-y)*(t) + (-x-5z)(exp(st)*t) + (3x-5y)(0) plug in x,y and z... dw/ds =...

Suppose w = x/y + y/z x = exp(t), y=2+sin(5t), and z= 2+cos(7t) A.) Use the chain rule to find dw/dt as a function of x, y, z, and t. Do not rewrite x, y, and z in terms of t, and do not rewrite exp(t) as x. I got this one right, the answer is 1/y*exp(t) +(- x/y^2+1/z)*(5*cos(5t)) +...

Hello everyone, our professor wanted us to find the vector chain rule proof and i found one here: http://web.mit.edu/wwmath/vectorc/scalar/chain.html But it makes no sense to me, where are the limits?

This is a problem that has stumped my entire class of Calc 1 students and two Calc 2 students. Find \frac {dy} {dx} y = \frac {(2x+3)^3} {(4x^2-1)^8} I know that the answer is (from the textbook, but I don't know how it got there) -\frac {2(2x+3)^2(52x^2+96x+3)} {(4x^2-1)^9}...

Please let me know if I derived this correctly (I did it a while back, and can't find the notebook): v(x,y)=u(r(x,y),s(x,y)) (derivations) At some point I come across this: \frac{\partial}{\partial x} \frac{\partial u}{\partial r} which I wrote as \frac{\partial^2 u}{\partial...

Let f: \Re^3 \rightarrow \Re be differentiable. Making the substitution x = \rho \cos{\theta} \sin{\phi}, y = \rho \sin{\theta} \sin{\phi}, z = \rho \cos{\phi} (spherical coordinates) into f(x,y,z), compute (partially) df/d(rho), df/d(theta), and df/d(phi) in terms of df/dx, df/dy...

I would like to prove a chain rule for limits (from which the continuity of the composition of continuous functions will clearly follow): if \lim_{x\to c} \, g(x)=M and \lim_{x\to M} \, f(x)=L, then \lim_{x\to c} \, f(g(x))=L. Can someone please tell me if the following proof is correct? I am...

Could someone please help me, I do not understand how the author of my textbook gets from one point to another. Here is the problem worked out, after the problem I will explain which part I don't understand. f(x)=x(x-4)^3 f'(x)=x[3(x-4)^2]+(x-4)^3 =(x-4)^2(4x-4) I do not understand how...

Please help me on this. I am trying to make and exercise from an author M.D. Hatton (an english). Let x = x(r, w) = r. cos (w) Let y = y(r,w) = r. sen (w) Let V = V(x,y). So V depends on r and w. By chain rule (I put "d" for the partial derivative) dV = dV . dx + dV. dy --...

Hi, I have 2 questions: 1. partial fractions: if I have following integral: Itegral[(1-2x^2)/(x - x^3)]dx; my question is do I break down the denominator to x(1-x^2) or do I go further: x(1-x)(1+x); this way it becomes more complicated; 2. chain rule: how does chain rule work in this...

Ok so I am reviewing multivariable now that i have some time; (why is it taking me so long to grasp some of these concepts!? :mad: ) anyways, and I am reading the proof of stokes theorem. The book I use is Stewart, but it seems to be ripped off word for word from swokowski, which in turn rippes...

If I was trying to prove the chain rule for partial derivatives, can I start with the definition of a total differential? What I mean is: Let f(x,y)=z where x=g(t) and y=h(t). I'm looking for \frac{dz}{dt}. By definition, dz = \frac{\partial z}{\partial x}dx + \frac{\partial...

Hi, I've seen a couple of proofs for the chain rule, and I know this probably sounds stupid, but I'm wondering why it can't be proved as follows: given the real valued functions y=f(u), u=g(x) since dy, du, dx, are all real valued functions as well can't you just state...

Original question: Let w = y^2 + xz. If x = rcos(theta), y = rsin(theta), and z = z, find (partial w)/(partial r) and (partial w)/(partial theta). Could someone please check my answers? (partial w)/(partial r) = zcos(theta) + 2ysin(theta) (partial w)/(partial theta) = -rzsin(theta)...

Hey what's up, The problem is...find the derivative of: y= x^2 sec(x-5) My question is...Would I start off by using the product rule and combine the chain rule with it, with x-5 being the inner function and sec(u) being the outer function? thanks...

Hey what's up, I had a question on the chain rule...How would I use the chain rule on a quotient...like if i have 1/(t^4 + 1)^3 , Would I use the quotient rule first, or just start with the chain rule?

Does anyone know how to do this with chain rule? If a cone has height 1 m and radius 30 cm, and the height is increasing at a rate of 1 cm/s, whereas the radius is decreasing at a rate of 1 cm/s, what is the rate of change of the cones volume? Solve the problem using the chain rule...

Can someone give me hints on how to prove the chain rule? I want to be able to learn this. Let h(x)=f(g(x)), then h'(x)=\lim\limits_{h \to 0}\frac {f(g(x+h))-f(g(x))}{h} But what now?