Partial derivative Definition and 363 Threads

So I don't understand why if you have something like U(x,y) = f(y+2x) and you take \frac{\partial U}{\partial x} = \frac{\partial f}{\partial x} you get \frac{df}{d(y+2x)} * \frac{d(y+2x)}{dx} Why does the partial derivative just change to the total derivative for one variable? It...

Homework Statement I can't seem to find information on this specific question i have. So I'm taking the partial derivative of this equation for both x and y I know how to do it for y, but I am not seeing something with respect to x fx(x,y)= x^7 + 2^y + x^y Homework Equations The Attempt at...

The problem is from an online homework assignment. I know it's probably fairly simple, but my brain isn't grasping it right now for some reason.[The Problem] We know: r(t) = <3t2 - 8t + 3, -9t2 + 2t + 7> And we are asked to find d2y/dx2.[Background Information] My understanding of d2y/dx2...

Homework Statement I have attached a picture of the problem. The question is the first one. Homework Equations The Attempt at a Solution I tried subbing u and v into the right hand side of the equation. I expanded and simplified but I do not think that is the right way to go...

Homework Statement A scalar field is given by the function: ∅ = 3x2y + 4y2 a) Find del ∅ at the point (3,5) b) Find the component of del ∅ that makes a -60o angle with the axis at the point (3,5) Homework Equations del ∅ = d∅/dx + d∅/dy The Attempt at a Solution I completed part a: del ∅ =...

Homework Statement Rewrite this in terms of f, f, ∂f/∂x, and x: ∂f(x,y)/∂(%Δx) = ∂f(x,y)/∂(d log(x) ) Homework Equations ∂(%Δf(x,y))/∂(%Δx) = ∂logf(x,y)/∂log(x)= ∂f(x,y)/∂x*x/f(x,y). ∂f(x,y)/∂log(x)=x∂f(x,y)/∂x The Attempt at a Solution I found that (%Δx) can be written as...

let f(x, y') = x + y' where y' = dy/dx then is it true, and why, that the partial derivative of f with respect to y' = 1 in this case we consder dx/dy' = 0, as if they are independent of each other.

Given that the Van Der Waals equation is (p + (an^2)/v^2)(v-nb)=nRT where n,a,R and b are constants... How to we find the derivative of p wrt v ? How to find the derivative of p wrt T without further differentiation ?? Can anyone teach me how to do this question ? Sincerly thanks~

Homework Statement The question asks: f(x,y) = 3xy+5y^3/[x^2+y^2] when (x,y) =! (0,0) f(x,y) = 0 when (x,y) = (0,0) what is df/dy at (0,0)? Homework Equations The Attempt at a Solution I'm not sure what the answer is. At 0,0 f(x,y) is 0, so it's simply a point and the...

Hi, I would like to confirm that I have understood this correctly. The steps to find local maxima/minima of a function f(x1, ... , xn) are: 1) We find all the stationary points. 2) We form the Hessian matrix and calculate the determinants D1, D2... Dn for a stationary point P we want to check...

Homework Statement Given that the surface (x**5)(y**2)+(y**5)(z**3)+(z**3)(x**2)+4xyz=7 has the equation z=f(x,y) in a neighbourhood of the point (1,1,1) with f(x,y) differentiable, find the derivatives (∂**2f)/(∂x**2) at (1,1) Homework Equations The Attempt at a Solution I...

Homework Statement How does ∂aAb behave under coordinate transformations in special relativity? Work out ∂'aA'b Homework Equations The Attempt at a Solution I have been given back the solution sheet to this problem, but I don't understand it. This is what I have I get...

I have the equation \frac{d\rho}{dt}=-\nabla\cdot\rho v where the vector v depends only x and t. I want to take the partial derivative of this whole equation with respect to t. Just not sure how to take the partial of the divergence. Thanks!

Homework Statement Consider z=sin(x+y+z). This defines z implicitly as a function of x and y. Find an expression for dz/dx The Attempt at a Solution This was on a test, this is what i did. I got 7/11 pts dz/dx = cos(x+y+z)*(1+(dz/dx)) (dz/dx) / (1 + (dz/dx)) = cos(x+y+z) i...

Homework Statement Calculate the partial derivatives (∂f/∂x & ∂f/∂y) Homework EquationsThe Attempt at a Solution really confusing me with the use of the summation and power to 3/2. This is my attempt, most definitely wrong but still tried. ∂f/∂x = x + c1*(2*(x-x1))*([( x-x1 )^2 +...

Homework Statement Find the second partial derivative of v=e^(x*e^y) Homework Equations I know that I need to find Vx and Vy first and then the second partial derivative would be Vxx, Vyy, Vxy. The Attempt at a Solution I'm really confused on how to find Vx or Vy Vx= the...

Homework Statement Stumped. Integral: f(x,y) = ∫ (from 1 to xy) of e^(t^2)dt find both fx and fy The Attempt at a Solution I've come up with: fx(x,y) = ∂/∂x ∫ (from 1 to xy) of e^(t^2)dt Not sure where to go... possibly take the integral, the take the partial derivative? I...

Does anyone know how to take the partial derivative of a convolution integral where the derivative is taken with respect to one of the functions of the convolution integral? In the following example, the best I can come up with is: \frac{\partial}{\partial g(t)}\int...

I am facing some problem about derivatives in spherical coordinates in spherical coordinates: x=r sinθ cos\phi y=r sinθ sin\phi z=r cosθ and r=\sqrt{x^{2}+y^{2}+z^{2}} θ=tan^{-1}\frac{\sqrt{x^{2}+y{2}}}{z} \phi=tan^{-1}\frac{y}{x} \frac{\partial x}{\partial r}=sinθ cos\phi then \frac{\partial...

Homework Statement I am working on a homework problem involving partial derivatives. I've been checking my answers against what Wolfram Alpha spits out just for extra assurance. For the following problem Find all the second partial derivatives: v = \frac{xy}{(x-y)}. When I get to the...

Homework Statement Let f(x,y)=1−x^{2}−y^{2}. Find the point at which \frac{\partial f}{\partial x} = \frac{\partial f}{\partial y} = 0 and illustrate graphically the nature of the surface z = f (x, y) at this point. The Attempt at a Solution Just did the partial derivatives and got...

Can someone please explain to me the difference between a regular derivative and a partial derivative?

1. Homework Statement Given y = xz5 and x = zg find : (∂y / ∂x)z (∂y / ∂x)g 2. Homework Equations 3. The Attempt at a Solution I understand the concept of a partial derivative, but I've never seen one such that there is a variable held fixed, or one where ∂x is not changing...

Homework Statement Given y = xz5 and x = zg (where g is some constant) find : (∂y / ∂x)z Homework Equations The Attempt at a Solution I understand the concept of a partial derivative, but I've never seen one such that there is a variable held fixed, or one where ∂x is not changing...

Homework Statement For the van der Waals equation of state, confirm the following property: (∂P/∂T)V (∂T/∂V)P (∂V/∂P)T = -1 Homework Equations The van der Waals equation of state is: P = nRT/(v-nb) - an2/V2 *R, n, a, b are const. The Attempt at a Solution I...

Homework Statement So the example says fx(0,0)=0 and fy(0,0)=0 (the partial derivatives). When I try it I'm getting functions that are not defined at (0,0): f(x,y)=xy/(x^{}+y^{}) so for example, fx=[x(x^2+y^2)-2y(xy)]/(x^2+y^2)^2 fx=(x^3+xy^2-2xy^2)/(x^2+y^2)^2...

Homework Statement In books I have been using to learn about the Lagrangian function, I find equations that have a derivative of a partial derivative, as in the snippet below. Is there a place where I can learn how this works and *why* it works? I think I can do it mechanically but I want...

Suppose we have a function u=f(x,y,z) If \frac{\partial u}{\partial x} = 0 then u is independent of x and is u=f(y,z) only. Correct?

For the equation: h(x,y,z)=y/(x+y+z) using quotient rule: f(y)=y g(x,y,z)=x+y+z hy = (x+y+z)(1)-(y)(1) / (x+y+z)2 = x+z / (x+y+z)2 I am getting the correct answer when evaluating at a point, but is this differentiation correct? More specifically, when using the quotient rule for...

I'm trying to figure out Ch 4, Sec. 7, Q 25.c of Mathematical Methods in the Physical Sciences, 3rd Ed. It's not homework I'm working on since I'm not in school. Assume that f\left(x, y, z\right) = 0 If x, y and z are each functions of t, show that \left(\frac{\partial y}{\partial...

Hello! I am trying to solve the partial derivative 'P' http://www.flickr.com/photos/61865210@N07/5757168138/ , which is part of a larger equation: http://www.flickr.com/photos/61865210@N07/5757300018/ (Sorry, can't seem to display to pictures, using insert image) Someone told me that solving...

hello,everyone,I'm from Shanghai, china.I got a problem when i was reading papers.I can't understand what is the partial derivative of a domain.I suppose it may be a curve,but exactly which curve it is? thank you very much!

Lets say I am having 2 vector a(x,y) and b(x,y) and i were to take : 1)the partial derivative of a(x,y) with respect x multiply by b(x,y) - b*(da/dx) will this be equals to a*(db/dx)

As we know, the inverse of a derivative is an integral and visa versa, but what's the inverse of a partial derivative? Is it even possible to un-do a partial derivative? Thanks for your help as I've been thinking about this for a couple days now!

This is a question from my calculus book that i thought was interesting, its not homework but I am curious to how you go about showing it. Show T (∂P/∂T)(∂V/∂T)=NR We know PV=NRT so if we take a partial how does the T end up on the other side?

Hi, I faced a problem (in Mathematica) when trying to plot a partial derivative of a functiona (of two variables) obatined by "Interpolation". More precisely, here is my input: surf=Interpolation[{ {{160.0, 160.0}, 2.852688}, {{160.0, 170.0}, 2.827547}, {{160.0, 180.0}, 2.818931}...

Homework Statement Suppose that the equation f(x,y,z)=0 can be solved for each of the three variables as a differentiable function of the other two. Prove that: (dx/dy)(dy/dz)(dz/dx)=-1 Homework Equations The Attempt at a Solution In the case of two variables where one is a...

g = u + Pv - Ts To find the partial derivative of g with respect to T at constant P, we do the following. dg = du + vdP + Pdv - Tds - sdT and du = Tds - Pdv. Therefore, dg = vdP - sdT. At constant pressure, dg = - sdT. Therefore, the partial derivative is - s. I think we could...

Homework Statement I need to find the partial derivative of the following, with respect to x q(x,y,e(x,y,u)) where e(x,y,u) is a function Homework Equations The Attempt at a Solution Well, the problem is I don't have a clue how to solve using just the function notation - I'm...

I'm trying to find the partial derivative of Q with respect to w0 and then set it equal to 0 and solve for w0. Finding the partial derivative was easy, but once I've got it, I'm having a hard time getting w0 by itself. Here's the original equation: Q(w_{0},w_{1},w_{2},w_{3})=\sum\left(y_{i}...

Homework Statement I have two problems where there is a critical point of f(x,y) at (0,0), but the second derivatives and mixed second derivative are all zero. The second partial derivative test is therefore inconclusive- all the information I can find online/in my notes just says it is...

Homework Statement I am working on some PDE's where we are doing Laplacian's in various coordinate systems and got stuck on a partial derivative of all things. It's been a while and it seems I have forgotten how to do them. Homework Equations I have the equation u(x,y)=\frac{1}{\sqrt{x^2...

Homework Statement Say that f(x) is some function whose second derivative exists and say u(x, t)=f(x + ct) for c > 0. Determine \frac{\partial u}{\partial x} In terms of f and its derivatives. Homework Equations PD Chain rule. The Attempt at a Solution Say that x and y are...

Homework Statement I am doing some gradient questions and having a little trouble understanding the partial derivatives to obtain the gradient. Most particularly in this question: f(x,y) = \frac{1}{3}(x^{2}+y^{2})^{2} Homework Equations So to find the gradient we take the partial...

Homework Statement Well hello! :smile: I am still uncomfortable with partials. In my (fluid mechanics) text we introduce this "stream function" \Psi(x,y) such that u =\partial{\Psi}/\partial{y} and v =-\partial{\Psi}/\partial{x} where u and v are the horizontal and vertical components of the...

I have a problem where part of the solution involves taking the Curl of the partial derivative of a scalar. If A is a scalar function, then wouldn't taking the partial derivative of A with respect to time "t" just give another scalar function?

Homework Statement Find the partial derivative with respect to x of sin(xyz - 1) Homework Equations None needed. The Attempt at a Solution I took the answer to be yz*cos(xyz - 1), but wolfram alpha is giving me yz*cos(1 - xyz). Anyone know what's going on here? Thanks!

Hello, I'm trying to proof the partial derivative definition , how do i proof it ?? @f/ @x = lim h-->0 lim [f(a +h, b) - f(a, b)] / h If possible , i'd like to seen all the calculations Best regards

Homework Statement I have some function f(x,t) and I know that both x and t undergo a coordinate transformation according to x = x' + Vt' and t = t'. I am asked to find \partial(f)/\partial(t') Homework Equations Chain rule of calculus The Attempt at a Solution Is...

So, my complex analysis professor defined \partial f / \partial z^* as \frac {\partial f}{\partial z^*} = \frac {1}{2} \left( \left(\frac {\partial u}{\partial x}-\frac {\partial v}{\partial y}\right) + i\left(\frac {\partial u}{\partial y} + \frac {\partial v}{\partial x}\right)\right) where z...