Chain rule Definition and 505 Threads

Homework Statement 6. A particle of mass m moves along a frictionless, horizontal plane with a speed given by v(x) = α / x. Where x is the distance of the object from the origin and α is a constant. Working with F = ma, we want to get the acceleration. You have v = v(x). You...

u^{*}(r^{*},\theta^{*},\phi^{*}) = \frac{a}{r^{*}}u(\frac{a^{2}}{r^{*}},\theta^{*},\phi^{*}) \frac{\partial u^{*}}{\partial r^{*}}= \frac{a}{r^{*}}u_{r^{*}} \left( \frac{a^{2}}{r^{*}},\theta^{*},\phi^{*}\right) \left( -\frac{a^{2}}{r^{2*}} \right) - \frac{a}{r^{*2}} u \left(...

Q. f(x)=ln (12x-5/9x-2) So by using the chain rule, i can get: (-4/3)((9x-2)2/(12x-5)2) and by using the quotient rule, i can get the final answer, which is: (2(-36x-8)(-36x-15)2-2(-36x-15)(-36x-8)2) ------------------------------------------------------------------...

Homework Statement d/dx (cos2x*sinx) The Attempt at a Solution Does this equal cos3x-2sin2x*cosx ?

Homework Statement If V=x^{3}f(y/x) show that x^{2}Vxx + 2xyVxy + y^{2}Vyy = 6VThe Attempt at a Solution i would normally just use the chain rule to differenciate this with respect to x and then so on but the f(y/x) is throwing me. Do i just treat the f like a constant or is it a whole new...

Wave on a string and the chain rule...Argh So, I am working through the wave equation for a review before my friend and I go off to grad school. It has been a couple of years since we both graduated with our BS in Physics. So, here is the question: Suppose I want to solve the wave...

So, I am working through the wave equation for a review before my friend and I go off to grad school. It has been a couple of years since we both graduated with our BS in Physics. So, here is the question: Suppose I want to solve the wave equation using a change of variables. Let's use...

If P: R2 -> R is defined by p(x,y) = x . y, then Dp(a,b)(x,y) = bx + ay. Please tell me in words how to read Dp(a,b)(x,y). Is this a product? a composition of functions? Is this the differential of p(x,y) at (a,b)? If that's the case, why does the text also state: If s: R2 -> R...

Homework Statement Use the Chain Rule to prove that for rectilinear motion, when the acceleration is a known function of position, you can find the velocity as a function of position via the integral \frac{v^{2}-v_{0}^{2}}{2} = \int^{s}_{s_{0}}a(s)ds Homework Equations...

Homework Statement y= squareroot tan(sin^2 x) Homework Equations chain rule The Attempt at a Solution f(x)= sqaureroot tan x g(x)= (sinx)^2 f'(x)=1/2 sec^2x ^1/2 g'(x)= 2 * sinx * cosx I don't know if my f'(x) is right if it is then do i just do the chain rule?

Given that F = \int{f[h(s),s]ds} does \frac{\partial}{\partial h}ln(F)=\frac{1}{F}\frac{\delta F}{\delta h}=\frac{1}{F}\frac{\partial f}{\partial h} ?

use chain rule to evaluate partial derivative of g with respect to theta at (r,[theta])=(2*sqrt(2),pi/4), where g(x,y) = 1/(x+y^2), x=rsin[theta] and y=rcos[theta] [b] r^2=x^2+y^2 and tan[theta]=y/x [b] The Attempt at a Solution I understand how to use the chain rule for partial...

Can anyone see where the flaw is in the development below, where I prove that (g o f)'(x)=g'(f(x)) instead of g'(f(x))f'(x), as it should be. Consider the usual hypothese under which the chain rule for real-valued function applies. Consider \epsilon>0. Since g is differentiable at f(x_0)...

Homework Statement (2x^2 - 3x + 1)(4x^3 + 4x -3)^5 Homework Equations The Attempt at a Solution

Hi 2 questions having a mental block and can't figure them out any help would be apprieciated Q1 differentiate f(x)=ax(2x+b)^7 where a and b are constants Q2 differentiate f(x)=(x^2+cos^3(x^4))^10 thanks for any help cheers

Homework Statement A function is called homogeneous of degree n if it satisfied the equation f(tx,ty) =t^(n) f(x,y), for all t, where n is a positive integer and f has continuous 2nd order partial derivatives. If f is homogeneous of degree n, show that df/dx (tx,ty) = t^(n-1) df/dx(x,y)...

Homework Statement Since both my questions are on the same topic, i'll throw them both in here 1. Find dz/dt for z=(x^2)(t^2), x^2+3xt+2t^2=1 2. Show that if u=xy, v=xy and z=f(u,v) then: x.dz/dx-y.dz/dy=(x-y)dz/dv Homework Equations The Attempt at a Solution 1. I only...

ok so f(g(x)) = x, for all x. f(3)=8 f'(3)=9 what are the values of g(8) and g'(8) ok, so g(8) = 3 because f(g(8)) must equal 8, and f(3) = 8, so g(x) must equal three. however, i have NO idea how to do g'(x) i was thinking of using the chain rule, but this gets me nowhere..help...

Homework Statement I'm working on a quick problem regarding a presentation that I'm giving, but I've come across an issue that I can't seem to resolve. Namely \displaystyle \left. \frac{d}{dt} \right|_{t=0} f(\phi^p (t+t_0) ) = \left( \phi^p \right) ^\prime (t_0) f Does anybody see...

How would you compute the derivative of cos(t^3)? Would you use the chain rule? Does anyone have a good way of recognizing when to use chain rule and when not to?

I am trying to find the first and second derivative using the chain rule of the following: u sin(x^2) This is what I have but I don't think it is correct. Can someone pls let me know? first derivative: u * 2x cos(x^2) + sin(x^2) u' second derivative: u * 2( x * -2sin(x^2) +...

I am trying to find the first and second derivative using the chain rule of the following: u sin(x^2) This is what I have but I don't think it is correct. Can someone pls let me know? first derivative: u * 2x cos(x^2) + sin(x^2) u' second derivative: u * 2( x * -2sin(x^2) +...

id like some help deriving certain functions using the chain rule the way our teacher does it is different from what the textbook says he derives the outermost functions before getting to the innermost functions, this is where i get confused =( for example f(x) = sincos(5x) i get...

http://math.berkeley.edu/~theojf/Midterm2Practice.pdf can someone please help me on problem number 2 of the link above? apologies for the bad handwriting. my professor is just horrible with that. i've done max and min with multivariables before and I've done chain rule , but I've never...

The question and my workings are attached:

y=2x^{sinx} i know i should use the product rule within a chain rule. but how can i use chain rule with sinx is the anwser y=-2x^{cosx} can anyone give me pointer to this easy problem and tell if am forgetting something.

Homework Statement A: Write f(x) = \sqrt{5-x^{2}} as a composite of two functions. B: Use the Chain Rule to find the derivative of f(x) = \sqrt{5-x^{2}} Homework Equations Chain Rule: y`= \frac{dy}{du} \frac{du}{dx} The Attempt at a Solution A: y = \sqrt{u} u = 5 -...

[SOLVED] another chain rule: easy one y=xe^{-x^2} i have no i dea how to start. f'= x^{x^2} or -2x^blah blah blah just get me started and i'll promise you i will finish it myself

[SOLVED] first derivative: chain rule: easy for you guys Y=E^(-mx) f= E^x g= -mx f'= E^x g'= o E^(-mx) * 0(E^(-mx)) i think, not sure though Y'= 0 which is wrong someone help

Hi guys, please see attachment Basically, could somebody please explain to me how I find {\varphi}_u_u, I really don't understand how it's come about. Apparantly I need to use the chain rule again and the product rule but I don't understand how to, if somebody could show me explicitly how to...

I have a question more than a problem to answer. I'm having a difficult time recognizing when to use the product rule and when to use the chain rule. How do you recognize when to use each, especially when you have to use both in the same problem. Problems like y+x^4y^3-5x^6+3y^8-42=0 tend...

This is supposedly the chain rule with functional derivative: \frac{\delta F}{\delta\psi(x)} = \int dy\; \frac{\delta F}{\delta\phi(y)}\frac{\delta\phi(y)}{\delta\psi(x)} I have difficulty understanding what everything in this identity means. The functional derivative is usually a derivative...

[SOLVED] Chain rule problem with partial derivatives Homework Statement Suppose that z = f(u) and u = g(x,y). Show that.. \frac{\partial^{2} z}{\partial x^{2}} = \frac{dz}{du} \frac{\partial^{2} u}{\partial x^{2}} + \frac{d^{2} z}{du^{2}} \frac{(\partial u)^{2}}{(\partial x)^{2}}...

Homework Statement Given z= square root of xy, x = 2t - 1, y = 3t +4, use the chain rule to find dz/dt as a function of t. Homework Equations The Attempt at a Solution dz/dt = partial derivative of z with respect to x multiplied by dx/dt + (partial derivative of z with respect...

Higher Partial Derivatives & Chain Rule (urgent) I'll have a test this evening, and I don't want to fail on a question like this, so please help me out! I will greatly appreciate for any help provided. The question: http://www.geocities.com/asdfasdf23135/advcal11.JPG My attempt...

Homework Statement the problem asks: Find \deltaf/\deltax and \deltaf/\deltay at x=1 and y=2 if z=f(x,y) is defined implicitly by 2x^{}2y/z + 3z/xy - xy\sqrt{}z = 3. Note that (1,2,4) is a point on the surface. Homework Equations Im not really sure how to approach this one. The...

Homework Statement the problem asks: Find \deltaf/\delta/x and \deltaf/\deltay at x=1 and y=2 if z=f(x,y) is defined implicitly by 2x^{}2y/z + 3z/xy - xy\sqrt{}z = 3. Note that (1,2,4) is a point on the surface. Homework Equations Im not really sure how to approach this one. The...

I am having a terrible hard time with the multivariable chain rule and its related stuff (I read my textbook many times, but it doesn't help that much because the explanations are very limited). I hope that someone can help me to withdraw from this darkness of confusion. 1) (Differentiation...

Hi everyone, I'm new to this forum... I hope I've posted in the right section... How do I differentiate y=2e(2x+1) using the chain rule? I let u= (2x+1) so du/dx = 2 but how do I differentiate y= 2eU ? thank you :)

Homework Statement The lengths a,b,c of a rectangle are changing with time. At the instant in question, a=1m, b=2m, c=3m and da/dt = db/dt = 1m/sec, and dc/dt = -3m/sec. At what rate is the box's volume changing at this instant? Homework Equations Chain rule for partial derivatives...

I'm trying to understand the proof for this theorem, and I can't see what they did to get from one step to the next. THEOREM: Suppose F(z) is an analytic function and that f(z) = F'(z) is continuous on a domain D. Then for a contour C lying in D with endpoints z1 and z2...

Homework Statement g(t) = 4ln(5ln(4t)) Homework Equations What is the derivative of g(t)? The Attempt at a Solution I have tried to use the chain rule in many different ways, and still can't come up with the correct answer. Anybody care to walk me through this? Is the...

Homework Statement I cannot believe I do not know this! dx/dt = dx/dt' dt'/dt is the chain rule for first derivatives d^2x/dt^2 = ? is the chain rule for second derivatives if it is complicated could you link me to a source that explains it please Homework Equations The Attempt at a...

Hmm, I've been working with functional derivatives lately, and some things aren't particularly clear. I took the definition Wikipedia gives, but since I know little of distribution theory I don't fully get it all (I just read the bracket thing as a function inner product :)). Anyway, I tried...

Homework Statement Find the integral of (Sin^4(x)*Cos^4(x)) in respect to x without using a calculator. Homework Equations Sin^2(x) + Cos^2(x) = 1 Sin^2(x) = (1-Sin(2X))/2 Cos^2(x) = (1+Sin(2X))/2 Sin(2x) = 2Sin(x)Cos(x) Cos(2x) = Cos^2(x) - Sin^2(x) The Attempt at a Solution...

Homework Statement y = (2x-3)/(x^2+4)^2 Homework Equations The Attempt at a Solution I am trying to relearn the calculus that I forgot from many moons ago. I am struggling with the chain rule in the above example. I tried to set it up as follows: This is what I know...

All the proofs I have found for the Chain Rule involve limits and the fundamental theorem of Algebra... So I came up with a PROOF, not a derivation. But my teacher claims that my proof is invalid. Is it? If so, why? let: u=z(x) y=f(u)=f(z(x)) therefore: dy/du = f ' (u) therefore...

im having a lot of trouble using the chain rule product rule and quotient rule..i can do them fine seperatly but when they're put together i can't get them like if you have (x^2-1)^4 (2-3x) i would start with 4(x^2-1)^3(2x)(2-3x)+(x^2-1)^4(-3) have i done something wrong here because i never...

Homework Statement y = 2x / (1+x^2)^2 Find dy/dx Homework Equations Chain rule The Attempt at a Solution I completely forgot how to apply the chain rule.. I mean, I can always apply the quotient rule, but I'm sure this is 1000 times easier if you can apply the chain rule. Do you...

When do you know to use the chain rule?? I really don't understand what this means: dr/dt = dr/ds * ds/dt Like in one example in the book they have: r(s) = cos2si + sin2sj + e^-3sk where s = t^4 Then they find dr/dt using the chain rule. My question is why can't you just...