Partial derivative Definition and 363 Threads

Homework Statement The elevation of a mountain above sea level at (x,y) is 3000e^\frac{-x^2-2y^2}{100} meters. The positive x-axis points east and the positive y-axis points north. A climber is directly above (10,10). If the climber moves northwest, will she ascend or descend and at what...

Find par(z)/par(t) at s=1, t=0 when z= ln(x+y), x=s+t, y=s-t Not sure how to approach cause if i plug in s's and t's i get an answer of 0 because taking the partial with respect to t yields a zero. Can someone shed some light on how to correctly solve? par(z)/par(t) = partial derivative...

Homework Statement Find the first partial derivatives of: 1. f(x,y) = x^y 2. u = x^(y/z) Homework Equations The Attempt at a Solution f_x = y*x^(y-1) f_y = lnx? u_x = (y/z)*x^((y/z)-1) u_y = lnx/z? u_z = ylnx/z? I'm not really sure how to do these right. =/ I...

Homework Statement The following contour diagram represents the function z = f(x,y) http://img15.imageshack.us/img15/9059/contour.th.jpg (a) Is z an increasing or decreasing function of x? I'd say it's increasing as it goes towards the x-axis the contour lines value goes down (b) Is z...

Homework Statement Let F(u,v) be a function of two variables. Find f '(x) for f(x) = F(x, 6). Homework Equations The Attempt at a Solution I need to find the answer in terms of F_u, how can I do this?

Homework Statement Homework Equations This should be easy, I don't know what I've done wrong... polar coordinates x=r cos(\theta) y=r sin(\theta) r^2=x^2+y^2 The Attempt at a Solution so with x=r cos(\theta) \partial{x}/\partial{r}=cos(\theta) \partial{x}/\partial{r}=x/r thus...

What does the notation \partial \betaD\alpha mean? I came across it in General Relativity, so I think it's the set of all partial derivatives of the vector function, i.e. \partial0D1, \partial0D2 and so on... but I'm not entirely sure.

If u : R^2 \to R has continuous partial derivatives at a point (x_0,y_0) show that: u(x_0+\Delta x, y_0+\Delta y) = u_x(x_0,y_0) + u_y(x_0,y_0) + \epsilon_1 \Delta x + \epsilon_2 \Delta y, with \epsilon_1,\, \epsilon_2 \to 0 as \Delta x,\, \Delta y \to 0 I know this can be proved using MVT...

If given an implicit function f(x,y,z)=0. Then, we can get z=g(x,y) and x= h(y,z). I know the answer for the partial derivative of g(x,y)' for x, how can I know the partial derivative of h(y,z) for z? I know f( x, y, z)=0. And I know ∂g / ∂x is positive. How can I define whether ∂h / ∂z is...

Find fyy (x,y) where f(x,y) = x2y3 + x4y + xe2y

Hi. I came across http://en.wikipedia.org/wiki/Second_partial_derivative_test" page on Wikipedia regarding the 2nd derivative test. It says that if the determinant of the 2x2 Hessian is negative, then f_{xx} f_{yy} < f_{xy}^2 So far, so good... But then it draws, seemingly from...

Through my learning of calculus, I have come under the impression that there is an important difference between the derivative of a variable with respect to another, and the partial derivative of a variable with respect to another. For example: I think that \frac{dy^2}{dx} = 2y\frac{dy}{dx}...

We found on-axis potential of a ring of radius R and Charge Q to be: V=(1/4pi*Epsilon naught) * (Q/sqrt(z^2 + R^2)) Find on axis electric field of ring of charge I know i just derive that equation, but am getting stuck. i got d/dz((1/4pi*Epsilon naught) * (Q/sqrt(z^2 + R^2)) Any...

Homework Statement Let : f(x,y) = \frac{xy(x^2 - y^2)}{(x^2 + y^2)^2} if (x,y) \neq (0,0) f(x,y) = 0 if (x,y) = (0,0) a) Find f_{xx}(0,0) b) Find f_{xy}(0,0) c) Find f_{yx}(0,0) Homework Equations None The Attempt at a Solution I'm not sure how to deal with the piecewise...

Homework Statement Show that the function is not differentiable at (0,0). f(x,y) = [ (xy)/(x2 + y2)(1/2) if (x,y) =/ (0,0) [ 0 if (x,y) = (0,0) The Attempt at a Solution I...

I just need to know what is/how to computer \frac{\partial f}{\partial x \partial y}

How is \frac{\partial}{\partial t} a vector? The original context of my question is located in post #5 of my most recent and very short-lived thread, “covariant vs. contravariant time component…”, located here https://www.physicsforums.com/showthread.php?t=261473 and it had to do with...

Homework Statement I have an initial data of d= 0.012608, V = 320 volt, Q = 1.50e-8 and A = 1.25e-4. y = Qd/AV. what is Δy , the partial derivative of y with respect to d? Homework Equations The Attempt at a Solution

I just handed in a homework where I used the assumption below ∂iuj∂jui=0 ? but when I start thinking about it I'm not so sure, could someone prove to me that it is zero? Or is that assumption totally off? Regards

I think the heading says it all. What happens if we take the partial derivative of a rate for example? eg \frac{\delta}{\delta t}(\frac{dx}{dt}) If it was normal differentiation with respect to t we'd get acceleration, or \ddot{x}. I read somewhere that the partial can be treated as...

Show that: \left(\frac{\partial z}{\partial y}\right)_{u} = \left(\frac{\partial z}{\partial x}\right)_{y} \left[ \left(\frac{\partial x}{\partial y}\right)_{u} - \left(\frac{\partial x}{\partial y}\right)_{z} \right] I have Euler's chain rule and "the splitter." Also the property...

Hello I have a question: Let w=2cot x +y^2.z^2 x = uv y = sin(uv) z = e^v Find the partial derivative of w releative to x.

For example, let f and g be defined as f=x^2 g=2xy I would say that the partial derivative of g with respect to y equals the perfect derivative of f(x). I've never been convinced that this is standard (or even correct) terminology. I am curious what some of you would use in place of perfect...

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 Given the partial derivative df/dx= 3-3(x^2) what is d^2f/dydx? I'm not sure if the answer would be 0, since x is held constant, or if it would remain 3-3(x^2) (since df/dx is a function of x now?)

[SOLVED] Partial derivative ... check me please f(x,y)=\sqrt[5]{x^7y^4} f_x(x,y)=\frac 1 5(x^7y^4)^{-\frac{4}{5}}(7x^6y^4) f_x(x,y)=\frac{7x^6y^4}{5\sqrt[5]{x^7y^4}} Correct?

Hi, I have a question about a certain step in the following problem/derivation, which you'll see in square brackets: Show that T * (\partial/ \partialT) = (-1/T) * (\partial/ \partial(1/T)) ["\partial/\partialT" is the operator that takes the partial derivative of something with respect to T]...

What's the difference between \partial ^2 x and \partial x^2 ? Is \partial ^2 x the same as \left( {\partial x} \right)^2 like \sin ^2 x$ is the same as \left( {\sin x} \right)^2 ? Thanks!

Hey everyone. I am new here and i have a problem with some partials. We're studying partial derivatives in calculus III. I understand and all, but we haven't covered how to take a partial derivative of an integral. This problem showed up in my practice problems before our exam tomorrow. The...

Homework Statement Given a graph of f(x,y), how can you determine where the partial and second derivatives are positive, negative, or zero? The attempt at a solution The first partial derivative is fairly easy to picture so I'm more concerned about the second partial derivative. I'm having...

Whoops got it now, didn't carry out my substitutions far enough. Homework Statement z = x^2 + 2y^2 x = rcos(\theta) y = rsin(\theta) Homework Equations The Attempt at a Solution Find (\partial z/\partial x) (theta is constant) dz = 2xdx + 4ydy dx = cos(\theta)dr - rsin(\theta)d\theta dy...

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...

partial derivative with respect to z & z_bar?? Hi, all.. While I`m reading the Ahlfors` complex analysis..I`ve found a tricky expressions about partial derivatives.. On the theory of analytic fns. author uses the expressions ∂f/∂z , ∂f/∂z_bar (z_bar - complex conjugate) with...

I'm confused on a procedural idea... If I'm doing the cross product of a gradient and 'the x component of a force' , so: \nabla X F(x) = \frac{\partial}{\partial z} Fy and Fy = x.. even though I am differentiating with respect to z , I am solving for an x component, which means...

Homework Statement d/dx 1/sin(y/2) The Attempt at a Solution this isn't an entire question, just looking for clarification about something. i have been asked as part of a larger question to find the partial derivative of 1/sin(y) with respect to x. in this case you treat y as a...

Homework Statement Calculate d\left\langle p\right\rangle/dt. Answer: Homework Equations d\left\langle p\right\rangle/dt = \left\langle -\partial V / \partial x\right\rangle The Attempt at a Solution I've been through the rigor down to getting \left\langle -\partial V / \partial...

Hi all. How to do the partial differentiation with this integral? (please see the attachment) I find no place to start tackling this problem...

Homework Statement Compute dv/dx and for v = [12xy-(x^2)(y^2)]/[2(x+y)] The Attempt at a Solution I attemptet to solve this problem just reading over partial derivatives for the first time and get the following answer: dv/dx (6y-xy^2)/(x+y)^2 let's say I take out the numerator and just took...

I'm using Griffiths' book to self-study QM and I'm having a slight problem following one of his equations. In page 11 of his "Intro to Quantum Mechanics (2nd ed.)", he gives the reader the following 2 equations: \frac {d} {dt} \int_{-\infty}^{\infty}|\Psi(x,t)|^2 dx = \int_{-\infty}^{\infty}...

\frac{\partial z}{\partial x}\cdot \frac{\partial z}{\partial y}=xyz^2 People,do we know how to solve this? I'm looking for the explicite solution z=f(x,y) so far I'm unable to solve this .Thinking of it for a half a day without much of the progress.Even though I haven't tryed all dirty...

Does anybody know if Mathematica can take the first, second, and third partial derivatives of a function? If it can, how would I go about doing so?

f(x,y)=2y / (y+cos x) .Find partial derivative w.r.t x can someone teach me how to do this pls thanx

f( x(1), ..., x(n) ) = sum (i=1) sin(x(i)^2) x(i) does anybody knows how to solve this pls

f(x,y)=arctan (y/x). may i know what is the first partial derivative of this?? thanx

Hi, What does it mean to put a partial derivative in first brackets and put a right subscript to it of another variable? (\frac {\partial Y} {\partial Y})_T Thanks. Molu

I've have met partial derivatives and the \nabla symbol, however, I was asked today what was the geometrical representation and meaning of \nabla \times r and \nabla \cdot r where r was a surface in 3D (i.e. r(x,y,z) = ...). For the first one, I think that the answer might be: \left(...

This is annoying me as i have the answer on the tip of my pen, just can't write it down. I'm not 100% sure i understand what the question is asking me to do. Consider the quantity u = e^{-xy} where (x,y) moves in time t along a path: x = \cosh{t}, \mbox{ } y = \sinh{t} Use a method...

Hi, I'm getting confused over a few points on the derivative of a parametric equation. Say we the world line of a particle are represented by coordinates x^i . We then parametrize this world line by the parameter t. x^i = f^i(t) . Now here is where I get confused. The partial...

In determining if a function is exact, here is the question. If V=V(T,P) and PV+RT, show that dV = R/PdT - RT/P2 dP. Is dV an exact differential? Do I go about by taking the derivative of R/PdT with respect to T, etc? I know this is not a difficult function, but I just want to make sure I'm...

I believe I have already found them for S and g, but I'm not sure how to do this for M2 and also M1 and M3.