Partial derivative Definition and 363 Threads

Homework Statement Let u(x,y) = f(x^3 + y^2) +g(x^3 + y^2) such that f and g are differentiable functions. Show that, 2y\frac{\partial u}{\partial x} - 3x^{2} \frac{\partial u}{\partial y} = 0 Homework Equations The Attempt at a Solution The part of confused about is how to...

Homework Statement Hello, recently in my calculus III class we went over some problems of the following form: If 'for some given equation' show: [FONT="Book Antiqua"][SIZE="5"]x(f[SIZE="2"]x) +y(f[SIZE="2"]xy) +f[SIZE="2"]x= 0 For some examples I was playing around with the operations...

Homework Statement Hello, I was given this complicated partial derivative to work out: z = √( 1-( (x+y)/(xy) )2 ) + arcsin (x+y)/(x-y) find: [SIZE="4"]fx and [SIZE="4"]fy and this is my final answer taking the partial derivative with respect to 'x' only right now...which is...

Homework Statement I have a problem where x = x1 + x2, and I need to relate d/dx to d/dx1 and d/dx2 somehow. Homework Equations The Attempt at a Solution I'm guessing there is a simple way to do this that I have just forgotten, I know how to find dx, but how can I find d/dx...

Homework Statement Let f(x,y)= 8x^{4} + y^{4} -2xy^{2}, what is \partial^{2} f/\partial x^{2} and \partial^{2} f/\partial y^{2} for the points where \partial f/\partial x = \partial f/\partial y = 0? Homework Equations The Attempt at a Solution The first partial derivative with...

Homework Statement m=a+b n=a2+b2 find partials (dm/db)a and (db/dm)n The Attempt at a Solution (dm/db)a = 1 is that right? and (db/dm)n I'm not sure how to get all the variables into one equation but a = sqrt(b2-n) so m = b - sqrt(b2-n) can someone...

Hello, So I have the function U(x,y). I have to find a partial derivative of U with respect to x. I understand that one can write that as U subscript x. But now I have to take d/dx of Ux, i.e. I have to take the derivative of Ux(x,y) with respect to x. Supposedly the answer is Uxx +...

Homework Statement find the partial derivative with respect to x Homework Equations f(x) = (alpha)x^2 alpha is a just to represent units N/m^2 The Attempt at a Solution well, i know that during a partial derivative all variable but the one of interest, x in this case, are held constant...

Homework Statement Show if v is harmonic ie. \; \nabla^2v=0 \; , then \nabla^2u=0 \hbox { where } u(x,y)=v(x^2-y^2,2xy) \nabla^2u=0 \;\Rightarrow\; u_{xx}+u_{yy} = 0 From the book: For u(x,y)=v(x^2-y^2,2xy) u_x=2xv_x + 2yv_y u_{xx} = 4x^2v_{xx} + 8 xyv_{xy} + 4y^2v_{yy} +...

x=rcos(θ), y=rsin(θ) Do these formulas look familiar? They give the relationship between two coordinate systems in the plane. Evaluate: |x'r x'θ| |y'r y'θ| I know that the x primes are cos(θ) and -rsin(θ), and the y primes are sin(θ) and...

Homework Statement Well, I'm not sure about this one. Its actually a differentiation problem, it asks me to determine if the function is differentiable at the given point. \sqrt[ ]{|xy|} at P(0,0) I think its not, but I must demonstrate, off course. So I try to solve the partial...

Homework Statement Well, it looks simple, but I'm not sure If the answer I'm giving is right. The function is: f(x,y)=\sin|y| And it asks for the partial derivatives, so: \displaystyle\frac{\partial f}{\partial x}=0 And \displaystyle\frac{\partial f}{\partial y}=\begin{Bmatrix}{...

Homework Statement (∂H/∂V)T Homework Equations PV = nRT H = U + PV n and R are constants

Homework Statement See uploaded image. Homework Equations n/a The Attempt at a Solution I’ve never seen this format so I am not sure what it is asking. Taking L1.B as an example. They are partials, but does it mean partial of x with respect to z? And then partial of y with...

Homework Statement See figure. Homework Equations The Attempt at a Solution Here's what I got, \frac{ \partial z}{\partial x} = \left( \frac{\partial z}{\partial u} \cdot \frac{\partial u}{\partial x} \right) + \left( \frac{\partial z}{\partial v} \cdot \frac{\partial...

Homework Statement Find the partial derivative with regards to vector r1 for the expression: theta = acos \frac{((r1-r2).(r3-r2))}{||r1-r2||*||r3-r2||} where "." is the dot product r1,r2 and r3 are positions in 3D-space. The expression above comes from the definition of the dot product...

Homework Statement [PLAIN]http://www.netbookolik.com/wp-content/uploads/2010/07/q1.png Homework Equations The Attempt at a Solution I thought, in order to take derivative function must be cont. so it would be nice to check limf as (x,y) goes to (0, 0) but it did not seem to...

well i have been trying to solve this equation and i just can't... the solution is given and it's at the second pdf file but i can't understand the procedure can somebody please help?

My textbook describes how some functions are not well approximated by tangent planes at a particular point. For example f(x)= xy / (x^2 + y^2) for x /= 0 0 for x = 0 at (0,0) the partial derivatives exist and are zero but they are not continuous at...

Can you give an example of a function f:X\times Y\to\mathbb{R}, where X,Y\subset\mathbb{R}, such that the integral \int\limits_Y f(x,y) dy converges for all x\in X, the partial derivative \partial_x f(x,y) exists for all (x,y)\in X\times Y, and the integral \int\limits_Y \partial_x...

Homework Statement G(\theta, k ) = \int^{\theta}_0 g(x,k) dx \frac{\partial G}{\partial \theta} = ? \frac{\partial G}{\partial k} = ? The Attempt at a Solution If I say that \int g(x,k) dx = H(x,k) \int^{\theta}_0 g(x,k) dx = H(\theta,k) - H(0,k) Then is...

Hello, I'm a first year physics student and in thermodynamics we always use \frac{1}{ \frac{dX}{dY} } = \frac{dY}{dX} and I was wondering 'how true' this is, i.e. what are the conditions for this to be true? For example, if I have the equation of state of a Vanderwaals gas: \left( P +...

Homework Statement f(x,y) = (x3+y3)^(1/3) Show that fy(0,0) = 1 The Attempt at a Solution fy=y2/(x3+y3)^(2/3) And...I take the limit of it as x and y goes to zero, which gets me 0/0

[SOLVED, THANKS]Differentation of Partial Derivative with respective to high order hi there, i am actually studying about functional equation. I got stucked with some derivatives problem, and where i could find nowhere to refer or study from, because it seems it is out of university book...

Hello, I have a simple question. Let's say we have a mechanical system with 2 degrees of freedom. Say the generalized coordinates (which are independent from each other in terms of constraints) are x and y. When we solve Lagrange-Euler equations for this system, we get time evolutions of...

Hi, why can I raise and lower indices of a partial derivative with the help of the metric tensor? E.g., wh is the following possible? (\phi is a scalar function) \partial^\mu \phi = g^{\mu\nu}\partial_\nu \phi -- derivator

I'm reading thru Brown's QFT. He uses the notation of the gradient operator or a partial differentiation operater with an arrow over the operator. The arrow points either left or right. Can someone please tell me what this means? thanks

Partial Derivative help! Find the first partial derivatives of f(x,y)=(4x+2y)/(4x−2y) at the point (x,y) = (2, 1). My professor never taught us how to do this so I have no idea where to start. Any help would be appreciated.

Homework Statement Given a body in a state of plane stress with no body forces where \sigmax=x2y \sigmay=(y3-3y)/3 Find \tauxy Homework Equations For plane stress \partial\sigmax/\partialx + \partial\tauxy/\partialy + X = 0 \partial\sigmay/\partialy + \partial\tauxy/\partialx +...

e^{10x -x^2 +4y -y^2} I don't know where to start. I have a gut feeling this might require the chain rule, but I don't know how to use it on this thing. I tried doing some silly simplification which resulted in a pair of quotients and products of exponentials and tried to derive those using...

Hi. I have been looking at differential forms, and that inspired me to consider a partial derivative as a ratio between cross products. Please tell me if the following makes sense. Say we have cartesian coordinates (x,y) and polar coordinates (\rho, \phi). I want to calculate...

Homework Statement I have John R Taylor "Classical mechanics" part 1, and I have an integral: \int\limits^{x_2}_{x_1}f\left(y+\alpha\eta,y^{\prime}+\alpha\eta^{\prime},x\right)\mbox{d}x and here is count derivative of underintegral function in \alpha \frac{\partial...

Homework Statement a and b are functions of z: a=a(z); b=b(z) I want to calculate the second order partial derivative operator on z Homework Equations Using the chain rule: \frac{\partial}{\partial z}=\frac{\partial a}{\partial z}\frac{\partial}{\partial a}+\frac{\partial...

Homework Statement Differentiate: y'''+ty''+y'+y'=0 Homework Equations The Attempt at a Solution I tried to use this definition: (y')'=y'' I'd be thankful, if somebody could show me the rules of differentiating y'.

Homework Statement 2 straight roads intersect at right angles. Car A, moving on one of the roads, approaches the intersection at 60km/h and car B moving on the other road, approaches the intersection at 80km/h. At what rate is the distance between the cars changing when A is 0.5km from the...

Homework Statement if (2,1) is a critical point of f and fxx(2,1)fyy(2,1) < (fxy(2,1))^2 then f has a saddle point at (2,1) Homework Equations The Attempt at a Solution i think its right but it turns out to be wrong can someone tell me why?

Homework Statement find the partial derivative of f(x,y)=(x^3+y^3)^(1/3) with respect to x and evaluate at (0,0) Homework Equations The Attempt at a Solution i found the general partial derivative with respect to x is (x^2)*(x^3+y^3)^(-2/3) if i plug in the point i would get zero...

Use the table of values of f(x,y) to estimate the values of each of the following partial derivatives. y=4.2 || 2.75262 ||| 0.27222 ||| 0.27107 y=4 ||| 5.74559 ||| 2.84839 ||| 0.64973 y=3.8 || 7.42708 ||| 5.84832 |||...

Homework Statement Find the first partial derivatives of the function. f(x,y) = definite integral (limits of integration x to y) cos(t^2) dt The Attempt at a Solution Is the partial derivative with respect to x just cos(x^2), and for y, cos(y^2) ? Or should the partial derivative...

There is a theorem in partial derivative If x= x(t) , y= y(t), z= z(t) are differentiable at t_{0}, and if w= f(x,y,z) is differentiable at the point (x,y,z)=(x(t),y(t),z(t)),then w=f(x(t),y(t),z(t)) is differentiable at t and \frac{dw}{dt}=\frac{\partial w}{\partial x}\frac{dx}{dt} +...

[b]1. Homework Statement I am suppose to use polar coordinate data to find derivatives, ie x = r cos(theta) y = r sin(theta) r^2 = x^2 + y^2 [b]2. Homework Equations show dtheta/dy = cos(theta)/r show dtheta/dx = -sin(theta)/r...

Given that f(x,y) = x|y| I know that fx(x,y) = |y| but what is fy(x,y). Thanks heaps.

Homework Statement Show \partial /\partial u \int_{a}^{u} f(x,v) dx = f(u,v) Homework Equations The Attempt at a Solution Basically i understand that we hold all other variables constant, and i understand that we will get our answers as a function of u and v. But to show that we have...

Homework Statement f(x, y) = \tan(x + y) \\ f_x = ? Homework Equations \frac{dy}{dx}\tan(x)= \sec^2 x The Attempt at a Solution I set y as constant, so I said derivative of y = 0 then took derivative of tan as above. However the answer should be f_x = \sec^2(x + y)...

Homework Statement what s the wrong with the following arguments suppose that w=f(x,y)and y=x^2 by the chain rule (for partial derivative ) Dw/Dx=(Dw/Dx)( Dx/Dx)+(Dw/Dy)(Dy/Dx)=Dw/Dx+2x( Dw/Dy) hence 2x( Dw/Dy)=0 ,and so Dw/Dy=0 Homework Equations The Attempt at a...

Homework Statement consider a function F : R^2 \rightarrowR^2 given as F(x,y)=(F1(x,y),F2(x,y)).Show that if F=\nablaf for some function f : R^2\rightarrowR,then (for partial derivative ) DF1/Dy=DF2/Dx show that F(x,y)=(ycos(X),xsin(y))is not the gradient of a function Homework...

Homework Statement A function f: R^n--R is homogenous of degree p if f( \lambdax)=\lambda^p f(x) for all \lambda\inR and all x\inR^n show that if f is differentiable at x ,then x\nablaf(x)=pf(x) Homework Equations The Attempt at a Solution set g(\lambda)=f(\lambdax) find out...

Homework Statement A function f(x) : Rn ->R is said to be differentiable at point \vec{a} provided that there exists a constant vector \vec{c} = (c_1, ... , c_n) such that lim_(\vec{h} -> 0) \frac{f(\vec{a}+\vec{h}) - f(\vec{a}) - \vec{c}*\vec{h}}{||\vec{h}||} Prove that if the...

I need some help with this partial derivative. I can do it by rules, but when I try and do it out using the definition of the partial derivative, I run into problems. Homework Statement Find the partial derivative of sqrt[x]y^2 - 4xy with respect to x The Attempt at a Solution Going...

Homework Statement According to the ideal gas law, the pressure, temperature, and volume of a gas are related by PV=kT, where k is a constant. Find the rate of change of pressure (pounds per square inch) with respect to temperature when the temperature is 300^{o}K if the volume is kept fixed...