Partial derivatives Definition and 435 Threads

Homework Statement The original problem: z=\sqrt{(x1-x)^2+(y1-y)^2}+\sqrt{(x2-x)^2+(y2-y)^2} Given that: ax+by+c=0, Find the minimum possible value of z. x1,y1,x2,y2,a,b and c are constants. The Attempt at a Solution I think I need to apply the partial derivative. I would get a...

EDIT: I got it! I just used implicit differentiation to find it. Thanks for looking in here everyone! x2+y2+z2=3xyz Find the partial derivatives: zx, zy, and zxy. Okay so I know how to find the partial derivative, but I am not sure as to if I need to get the z on one side by itself...

(x^2 + y^2)*e^(y^2 - x^2) I am having trouble finding the critical points. Fx=2xe^(y^2-x^2)(1-x^2-y^2)=0 Fy=2ye^(y^2 - x^2)(1+x^2 +y^2)=0 or 0=x(1-x^2-y^2) 0=y(1+x^2+y^2) now, finding all the roots is giving me trouble. x and y obviously = 0, but I am unsure how to move forward to...

Homework Statement Evaluate the partial derivatives ∂f/∂x and ∂f/∂y at the origin (0,0), where: f(x,y) = ((xy)^3/2)/(x^2 + y^2) if (x,y) ≠ (0,0); and f(0,0) = 0. Homework Equations ∂f/∂x(x0,y0) = lim(h->0) [(f(x0+h, y0) - f(x0, y0)) / h] ∂f/∂y(x0,y0) = lim(h->0)...

Find \frac{\partial y}{\partial x} of 3sin (x^2 + y^2) = 5cos(x^2 - y^2) \partial y = 6ycos(x^2 + y^2) - 10ysin(x^2 - y^2) \partial x = 6xcos(x^2 + y^2) + 10xsin(x^2 - y^2) so I thought \frac{\partial y}{\partial x} = \frac{6ycos(x^2 + y^2) - 10ysin(x^2 - y^2)}{6xcos(x^2 + y^2) +...

Homework Statement Knowing: y(x,t) = Acos(kx-ωt) Find the partial derivatives of: 1) dy/dt 2) dy/dx 3) d^2y/dt^2 4) d^2y/dx^2 Homework Equations The Attempt at a Solution These are the answers the actual answers: 1) dy/dt = ωAsin(kx-ωt) = v(x,t) of a particle 2) dy/dx =...

Homework Statement If z = ax^2 + bxy + cy^2 and u = xy , find \left(\frac{\partial z}{\partial x}\right)_{y} and \left(\frac{\partial z}{\partial x}\right)_{u} . Homework Equations I have Euler's chain rule, the "splitter" and the "inverter" for dealing with partial derivatives...

Homework Statement Two charges one located at P at the position (x,y,z) and P' at the position (x',y',z') Let f= 1/R. Calculate Fx= partial derivative of f with respect to x. Calculate Fx'= partial derivative of f with respect to x'. There are sub question involving the same thing with...

Homework Statement Car A is going north, car B is going west, each are approaching an intersection on their respective highways. At an instant, car A is .3km from its intersection while car B is .4 km from it's intersection. Car A travels at 90km/h while car B travels 80km/h. Find the rate at...

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...

Now in my textbook it shows the following partial derivative solution: \frac{d}{dx}(3y^{4} + e^{x} sin y) = e^{x} sin y I thought since it's meant to be the partial derivative in terms of x that the y variable would be untouched. What's happening?

Hello everyone, I am trying to take partial derivatives of the following equation and I am having difficulties. The partial derivatives are of Q w.r.t D, ΔP, ρ, and w. Any help would be much appreciated. Thank you. Paul

In the context of height fields, the geometric meaning of partial derivatives and gradients is more visible than usual. Suppose that near the point (a, b), f(x, y) is a plane (the above figure). There is a specific uphill and downhill direction. At right angles to this direction is a direction...

Homework Statement The temperature T at a location in the Northern Hemisphere depends on the longitude x, latitude y, and time t so we can write T=f(x,y,z); time is measured in hours from the beginning of January. Honolulu has longitude 158 degrees W, and latitude 21 degrees N. Suppose that...

Homework Statement Find the second partial derivatives. z= x/(x+y) The Attempt at a Solution I solved the correct df/dx, d^2f/dx^2, df/dy, and d^2f/dy^2, however I can't seem to get the correct answer for d^2f/dydx and d^2f/dxdy. My df/dx is y/(x+y)^2 which I changed to y((x+y)^-2)...

http://img132.imageshack.us/img132/5736/wathh1.jpg I think to find dz/dx (d = delta) first of all is by dz/dx = (dz/du)(du/dx) + (dz/dv)(dv/dx) But how do I find dz/du and dz/dv for this? I only have 1 example that resembles this and it had z defined as a function as z = u^v, but...

Homework Statement We are given a table where showing the points x and y and values of a function f(x,y). The function itself is not given. I have to find the partial derivatives f'x, f'y, f''xx, f''yy and f''xy around the point (2,3). Homework Equations I have to use the definition ...

I am really struggling with this h/w problem...especially the 1st part. Problem Statement: Consider the function f defined by f(x1,x2,x3)=cos(x1+x2)+exp(sin(x1*x2*x3)+cos(x1^{2}+x3^{2})). Show that the partial derivatives exist and are continuous everywhere. Solution 1- I can...

[SOLVED] partial derivatives Homework Statement Can the partial derivative of a function depend depend on the form it is in? Say, z = f(x,y), and y=g(x,w). If I take \frac{\partial z}{\partial y} then I get \frac{\partial f(x,y)}{\partial y} which is not necessarily 0. But...

[SOLVED] partial derivatives - verify solution? Let f:\mathbb{R}^3\rightarrow\mathbb{R}, g:\mathbb{R}^2\rightarrow\mathbb{R}, and F:\mathbb{R}^2\rightarrow\mathbb{R} be given by F(x,y)=f(x,y,g(x,y)). 1. Find DF in terms of the partial derivatives of f and g. 2. If F(x,y)=0 for all (x,y)...

Homework Statement Okay, so at my school, you can get into Diff EQs without taking Calculus 3. So, I get most of the basis of it, but some things I am missing the boat on. How does one go from d(\frac{1}{3}x^3y^3)=x^2y^3dx+x^3y^2dy ? How do you carry out that operator? It says to take...

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...

[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 Wheat production in a given year, W, depends on the average temperature T and the annual rainfall R. Scientists estimate that the average temperature is rising at a rate of 0.15 degrees celsius per year and rainfall is decreasing at a rate of 0.1 cm per year. The also...

[SOLVED] Partial Derivatives with Inverse Trig Functions Homework Statement Show that u(x,y) and v(x,y) satisfy the Cauchy-Riemann equations... \frac{\partial u}{\partial x} = \frac{\partial v}{\partial y} given that u = ln(x^{2} + y^{2}) and that v = 2tan^{-1} (y/x) Homework...

f(x,y) = (2xy)/(x2 + y2), 0 if (x,y) = (0,0) Now I'm supposed to evaluate this at (0,0). I take the first partial derivative and I get 0/0 but when I use the definition of derivatives I get a whole number. Why the hell is this?

[SOLVED] The partial derivatives of arctan(y/x) let w = arctan(y/x) the partial derivatives are: dw/dx and dw/dy i know that the derivative or arctan(x) is 1/(1+x^2). so for dw/dy, i get (1/ 1 + (y^2/x^2) ) * (1/x) = x/(x^2 + y^2) ? correct? how do i find dw/dx?

Hello, Can anyone please tell me how to get the relationship between partial derivatives at a point, that is, dy/dx|x = - df/dx|y / df/dy|x ?

I have to find the expansivity of a substance obeying the Dieterici equation of state using the cyclical relation. I understand what I need to do, but I'm having a problem with the partial derivatives of the equation of state. I was wondering if anyone could refresh me on how to take a...

[SOLVED] Partial Derivatives Whoops, never mind my calculus book explained it. Homework Statement F(x,y,z) = 0 (\frac{\partial x}{\partial y})\right)_{z} (\frac{\partial y}{\partial x})\right)_{z} = 0 Show (\frac{\partial x}{\partial y})\right)_{z} (\frac{\partial y}{\partial z})\right)_{x}...

Homework Statement Prove that if all partial derivatives up to order n are zero at \vec{x} and f(x) = 0 then \displaystyle\lim_{h \rightarrow 0} \dfrac{f(x + h)}{|h|^n} = 0 Homework Equations \displaystyle\lim_{h \rightarrow 0} \dfrac{f(x + h) - f(x)}{|h|} = 0 f(x) = 0 The Attempt...

[SOLVED] Partial Derivatives I'm having a bit of trouble on an old test problem. It states: Determine if there is a function f(x, y) such that fx(x, y) = yex + 1 and fy(x, y) = ex + cos(y). If such a function exists, find it. I know that such a function exists because fxy(x, y) = ex, and...

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...

http://www.geocities.com/asdfasdf23135/advcal9.JPG I find this question to be extremely challenging... The best I can think of is z=f(x,y)=ln(theta), would this work? Can someone teach me how to define S=domain of f? This problem is giving me bad headaches. It would be nice if...

http://www.geocities.com/asdfasdf23135/advcal4.JPG Let f(x,y)=depth. What I've seen in the model solutions is that they used the estimate that the partial dervaitve of f with respect to x evaluate at (0,0) is equal to [f(100,0) - f(0,0)] / 100 = 1/4, & the partial dervaitve of f with...

Homework Statement Homework Equations The Attempt at a Solution I follow the steps until I get to 2(x+y+z)(1 - sin(r+s) + cos(r+s)) The actual derivation process isn't the problem, I get lost in trying to figure out when to plug values for r and s.

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...

Homework Statement (Q) Express vx in terms of u an v if the equations x = v ln(u) and y = u ln(v) define u and v as functions of the independent variables x and y, and if vx exists. (Hint: Differentiate both equations with respect to x and solve for vx by eliminating ux. Homework...

I'm trying to show that the force F= k [x, 2y, 3z] (where k is a constant) is conservative. If I take the cross product of: \nabla x F, that equals \frac{\partial}{\partial y} F_{z} - \frac{\partial}{\partial z} F_{y} = \frac{\partial}{\partial y} k3z -...

Homework Statement Find the indicated partial derivative. u=e^{r\theta}\sin\theta; \frac{\partial^3u}{\partial r^2\partial\theta} 2. The attempt at a solution I started to derive u_{\theta} and I attained r*e^{r\theta}\sin\theta + e^{r\theta}\cos\theta But now I don't know how...

Homework Statement Given that mechanical equation of state for a paramagnetic substance is m=\left(\frac{DH}{T}\right) where D is a constant, H is the magnetic field, m is molar magnetization and the molar heat capacity c_{m} is constant, find entropy and enthalpy Homework Equations...

I am reading "Cracking the GRE Math Subject Test - Princeton Review, 3rd Ed." and and confused by the section on the chain rule for partial derivatives. The method in the book is as follows: 1) Draw a diagram to show how the variables depend on each other, with an arrow meaning "depends on"...

Find the four second partial derivatives for f(x,y) = y^2e^x + xycosx I am stuck on the last part... here's what I got so far: Zx = y^2e^x - ysinx Zxx = y^2e^x - ycosx Zxy = ? Zy = 2ye^x + xcosx Zyy = 2e^x + xcosx Zyx = ? I need help with solving for xy. Both should end up...

Homework Statement I would like to know how to solve the PDE \frac{\partial f}{\partial x}+\frac{\partial f}{\partial y}+\frac{\partial f}{\partial z}=g(x,y,z) * f is the unknown function * g(x,y,z) is a known and smooth function Homework Equations divf=g The Attempt...

Homework Statement there is a question and a solution in this page; http://www.fen.bilkent.edu.tr/~otekman/math102/s03/m2q5.html" Please firstly examine the question and solution. (5b)... There it says f(x,y)=z and x=g(r,teta) and y=h(r,teta) and asks fxx. He solves this problem by...

Has anyone evaluated the Einstein Field Equation purely in partial derivatives wrt x,y,z,t? What does it look like?

Homework Statement I've attactched an image of the question, I hope this is ok, if not let me know and I'll copy it out onto a post, The Attempt at a Solution I've done parts (a) and (b) using the total derivative of f ( http://mathworld.wolfram.com/TotalDerivative.html ) but I can't get...

im given the function f(r,a,b) and z=rcos(a) y=rsin(a)sin(b) x=rsin(a)cos(b) now i need to find the partial derivative of f'_y, without solving r,a,b in terms of x,y,z, what that i got is: f'_y=f'_a*a'_y+f'_r*r'_y+f'_b*b'_y the answer should include the derivatives of f wrt r,a,b, which i...

Ok, so not really partials, I know how to do those. But now in my math physics class we were introduced to a new notation where it's the partial with respect to a variable, with another variable held constant. This is the problem I am trying to do in the book: (\frac{\partial z}{\partial...

The problem is as follows: Cartesian and polar coordinates are related by the formulas x = r\cos\theta y = r\sin\theta Determine \frac{\partial r}{\partial x}, \frac{\partial r}{\partial y}, \frac{\partial\theta}{\partial x}, and \frac{\partial\theta}{\partial x}. Differentiate the...