Chain rule Definition and 505 Threads

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} =...

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 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...

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...

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 :-(

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...

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...

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...

Suppose I have F(x,y) and y=y(t) and x=x(t) Therefore, Ft = Fx*xt + Fy*yt. Right? Can I write Ftt = (Fxx*xt + Fyy*yt)*xt + Fx*xtt + (Fxx*xt + Fyy*yt)*yt + Fy*ytt ? Basically I'm trying to figure out the second derivative by chain rule.

If a function is given by u = u(T,v) how to use the chain rule to write how u changes with respect to T & v. Please specify the steps involved. i understand chain rule as [SIZE="4"]\frac{du}{dx} = \frac{du}{dy} \frac{dy}{dx}

Homework Statement If Z= F(x-y), show that Zx + Zy = 0 Homework Equations The Attempt at a Solution Suppose I let Q = x-y. Then, by chain rule, Fx(Q) * 1 + Fy(Q) * -1. By identity, this statement must hold for all values x,y. In particular, it must hold for x=y. By x=y...

Homework Statement So there is an exercise in which I should "verify" the chain rule for some functions. In other words to do it by substitution, then doing by the formula and checking if the results are the same. (and checking with the book`s answer too) For a few of them, they just don`t...

I was wondering how to prove the multivariable chain rule \frac{\mbox{d}z}{\mbox{d}t}=\frac{\partial z}{\partial y}\frac{\mbox{d}y}{\mbox{d}t}+\frac{\partial z}{\partial x}\frac{\mbox{d}x}{\mbox{d}t} where z=z(x(t),y(t)) I don't really need an extremely rigorous proof, but a slightly...

Homework Statement w= f(x,y) x = u + v Verify that Wxx - Wyy = Wuv y = u - v Homework Equations The Attempt at a Solution I know how to find Wu or Wv but I have no idea on how to proceed to find the 2nd order derivative (or 3rd,4rth etc.. obviously). I...

Hi there, My equation to solve is (xy+(x^2))dx + (-1)dy=0 For method of exact solutions, the partials are not equal to each other so I cannot use exact solutions (reverse chain rule) I don't know how to solve this

Homework Statement Find the derivative of the following: Homework Equations Y= x^3(5x-1)^4 The Attempt at a Solution 4(3x^2(5x-1)^3)(4(3x^2(3(5x-1)^2)(2(5x-1)(5)

Just some general questions as I'm confused with when to use chain rule when not to. For instance, to find the derivative of e^sqrt(x), the right answer is to use chain rule to get e^sqrtx*the derivative of sqrt(x). BUT, isn't there a formula that: d/dx K^x = In(K)*K^x? K for constant and x...

Homework Statement Calculate ∂f/∂s + ∂f/∂t at s = 2, t = -1. Given: f = f(x,y) x = s - t y = s2 + t2 ∂f/∂x (3,5) = 0.06170 ∂f/∂y (3,5) = 0.06170 Homework Equations ∂f/∂s = ∂f/∂x * ∂x/∂s + ∂f/∂y * ∂y/∂s ∂f/∂t = ∂f/∂x * ∂x/∂t + ∂f/∂y * ∂y/∂t The Attempt at a Solution...

I did a derivative problem, but my book says that my answer is wrong. f(x)=x2(x-2)4 I didn't see much use in the chain rule so I used the product rule. x2(4(x-2)3) + (x-2)4(2x) =4x2(x-2)3 + 2x(x-2)4 The book says that instead of this, the answer is ... x2(4(x-2)3(1)) + (x-2)4(2x) =...

Homework Statement http://images.calcchat.com/solutionart/etf5e/03/d/se03d01063.png Homework Equations The Attempt at a Solution I get to the third row, but can't simplify (Sin2θ)(Cos2θ). I'm looking at the trigonometric double angle formulas, and still can't figure out how the...

Homework Statement Suppose f(x,y) = 2x^5 + 4xy + 2y^3 g1(u,v) = u^2 - v^2 g2(u,v) = uv h(u,v) = f(g1(u,v), g2(u,v)) Use chain rule to calculate: dh/du (1,-1) and dh/dv (1,-1) Homework Equations The Attempt at a Solution i let h (u,v) = 2(u^2 - v^2)^5 + 4(u^2-v^2)(uv) +...

Homework Statement cot^2(Cos\theta)Homework Equations chain rule f prime (x) = f prime(g(x) * g prime (x) The Attempt at a Solution I am not sure if I am just inputting the wrong numbers into webassign or I am just missing and important trig derivative and just completely off of the boat...

I always get muddled when I'm dealing with chain rule of any degree of complexity and also when dealing with powers of trig. functions - this problem contains both: find \frac{\partial n}{\partial A} and \frac{\partial n}{\partial D} of the following function...

I'm curious if there's a chain rule for the commutator (I'll explain what I mean) just like there's a product rule ([AB,C]). So, say you have an operator, which can be expressed in terms of another operator, and we know the commutation relationship between x and another operator, y. I'll call...

Solve the following: d/dt cos(theta) d/dt t sin(theta) d/dt r cos (theta) d/dt r^2 (theta) d/dt e^ (-3x) d/dt (x^2 + y^2) I would assume all by the second one are 0 since your solving for terms dt and not theta, x, y, or r... I don't think its right at all. I know it goes something...

Hi, Say x=position, v=velocity, a=acceleration, t=time. Thanks! EDIT: I just realized that 2/x is not a constant and thus I shouldn't have treated it as a constant (taking the derivative of it as 0). However, I don't understand how to take the derivative with respect to t of it.

I want to find the second order derivative for f(x,y),x(u,v),y(u,v), f depends on x and y, and x and y depends on u and v. I'm trying to find \frac{{\partial^2 f}}{{\partial v \partial u}}This is what I did: \frac{{\partial f}}{{\partial u}}=\frac{{\partial f}}{{\partial x}}\frac{{\partial...

I'm confident in my math ability, but how is it that by using the chain rule... W_{x_1 \rightarrow x_2} = \int^{x_2}_{x_1} m \frac{dv}{dt} dx can be turned into W_{x_1 \rightarrow x_2} = \int^{x_2}_{x_1} m \frac{dv}{dx} \frac{dx}{dt} dx = \int^{v_2}_{v_1}mv dv ? I understand the...

From james stewart calculus Early Transcendentals.Before he states the proof he intoduced a property of differentiable funcion My problem is how we defined \epsilon to be 0 when \Delta x=0 where this is not in the Domain.

Is there an elegant and simple proof of the Chain Rule? Every proof I've found is complex and mind-boggling

Homework Statement Use the chain rule, the derivative formula Dxsinu=cosuDxu, together with the identities cosx=sin(\pi/2 -x) and sinx=cos(\pi/2 -x) to obtain the fomula for Dxcosx. Homework Equations Chain rule: dy/dx=dy/du\cdotdu/dx The Attempt at a Solution For my second...

Homework Statement Use implicit differentiation to find dy/dx 2x^3+x^2y-xy^3 = 2 Homework Equations Chain Rule et al. The Attempt at a Solution My questions is this. When deriving something like xy^3, apply the product rule to get 1y^3 + x\frac{d}{dx}y^3 I am confused on...

Homework Statement If u=f(x,y) where x=escost and y=essint show that d2u/dx2+d2u/dy2 = e-2s[d2u/ds2+d2u/dt2 The Attempt at a Solution i have no idea! question though, do the partial derivitives have to be solved and expanded then just show that one side equals the other or can...

Homework Statement \frac{d}{dx}(x+(x+sin^2(x))^3)^4 Homework Equations Calc up to Chain Rule. The Attempt at a Solution Using product and chain rule I got: \frac{dy}{dx}=4(x+(x+sin^2(x))^3)^3(1+3(x+sin^2(x))^2)(1+\frac{d}{dx}sin^2(x)) Then I calculated the derivative of sin^2(x)...

Homework Statement I have proven in two ways (correctly) that the derivative of ln|x| = 1/x (note absolute value does vanish) Now I open my textbook and see a general rule that \frac{d}{dx} ln (u) = \frac{u'}{u} And the not so general derivative of |x| is \frac{d}{dx} |x| =...

Hello! I'm currently taking Mth 251 and have been working on this chain rule for a bit. It's kind of straight forward, there's just a lot of chains inside of chains and so forth. I think I have a solution, but I'm not entirely sure its correct. Homework Statement Find the derivative of...

1. Derive arcsin(1 - 2 e ^-t) 2. The derivative of arcsin is 1/√(1-x^2) 3. I tried using the chain rule for 1 - 2 e ^-t, but that didn't work out. What should I take the chain rule of?

hi does anyone know why the 2nd derivative chain rule is as such? i roughly know that if u = f(x,y) and x=rcos(T) , y = rsin(T) then du/dr = df/dx * dx/dr + df/dy * dy/dr but if i am going to have a second d/dr, then how does it work out?