Partial derivatives Definition and 417 Threads

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...

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...

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...

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 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...

Ok i got this problem... T(x,y,z,t)= -2xy^2+e^(-3z)cos(5x-.75t) taking the partial derivative with respect to x first, so i break the problem apart with the left and right sign of the addition side so i get... -2y^2 for the left side and then am stubling on the right side, I am think just...

Okay, I have a question that I am not good enough at multivariable calculus yet to answer myself. Basically, say I have the following inequality: a < sin(xy)/y < b with a < b. How can I find out what the maximum value of y is on the interval 0 < y < 1 such that the above inequality...

I'm trying to follow a derivation in given in a textbook. Part of this derivation goes like this: \frac{d}{ds}\left(\frac{1}{c}\frac{dx}{ds}\right)=c\left(\frac{\partial^2\tau}{\partial x^2}\frac{\partial \tau}{\partial x} + \frac{\partial^2\tau}{\partial x \partial y}\frac{\partial...

sin(5x-4y+z)=0 how do I find \frac{\partial z}{\partial x}? if the problem is sin(5x-4y+z)=f(x,y,z), I can find \frac{\partial f}{\partial x} but I don't know what to do when it is just equal to zero.

This is the problem word for word out of my textbook: Given that z = \frac{x^3 + y^3}{x - y} , x = 10, y = 8, dx = 2, dy = -3, find dz. Hopefully, someone can tell me where my error(s) are. This is my method: z = \frac{x^3 + y^3}{x - y} \therefore z = x^3(x-y)^{-1} + y^3(x-y)^{-1}...

How do I go about proving the following partial derivitive is a linear operator? d/dx[k(x)du/dx)]

I'm working on this question, and I have no idea where they are getting this. They said to differentiate f(xt,yt) with respect to t where. Note: f_x denotes partial derivative with respect to x. The answer is coming up as, from the book... f_t * x * t^{(n-1)} + f_t * y * t^{(n-1)}...

8. Let f : R^3 → R a function all whose first order partial derivatives are continuous and such that f(0, 1, 1) = 0, f_x(0, 1, 1) = 1, f_y(0, 1, 1) = 2, f_z(0, 1, 1) = 3. Find lim t-->0 f(t2, cosh t, et) f(t, cos t, cosh t) 9. Let f : R2 → R such that f(x, y) = f(y,−x) for all (x, y) ∈ R2, and...

Greetings, I need help in finding the partials with respect to x and y at (x,y) =/= (0,0) and (x,y) = (0,0)... Let f(x,y) = { (xy^2-x^2y+3x^3-y^3) / (x^2+y^2) , (x,y) =/= (0,0) { 0 (x,y) = (0,0) There was a hint given...

Hello everyone I have no idea how to start this problem because I'm confused on the notation, what does it mean? here is a picture: http://img291.imageshack.us/img291/1177/lastscan2lc.jpg I know how to take partial derivatives, but the d^2 part is confusing and the dx^2? what the!

Hello everyone... I'm very confused... i'm suppose to find dz/dt and dw/dt but for some of the questions there is no w variable! so what do u put for dw/dt?! Also i have the following: w = xy + yz^2; x = e^t; y = e^t*sint; z = e^t*cost; so I'm trying to find dz/dt and dw/dt; dz/dt =...

Hello everyone,i had a question..i have the following problem, I'm suppose to find the first partial derivatives: f(x,y,z,t) = xyz^2*tan(yt); I got all the partial derivaties right but the fy, they get: fy = xyz^2*sec^2(yt); when i do it, i get: fy = xz^2*sec^2(yt)*t = txz^2*sec^2(yt)...

I'm trying to find the uncerainty for the following equation: e = Qd/AV, where Q is the charge in C, d is the distance in m, A is the area (Pi * r^2), and V is the voltage. I get something like delta_e = delta_Q/Q + delta_d/d + delta_A/A + delta_V/V but when I do that, I get a rather...

If sin (2x+4y+z) = 0 , find the first partial derivatives \frac{dz}{dx} at the point (0,0,0) A.) \frac{dz}{dx}(0,0,0) = _________________ isnt this saying get the derivative of z, respect to x? I'm just kinda confuse since the variable 'z' is also in the problem. well i got the...

On question If I have the plane z = y + f(x,y) where f(x,y) = sin(x) * y Is it possible to find the complete partial derivatives for z ? /Bob

In my differential equations book there is this step, that i don't know how it goes from one side to the next. (t^2)y' + 2ty = ((t^2)y)' cause, on the left side I factor out a t, and i get t(ty'+2y) ...so do i have to learn partial derivatives in order to get from the left side to the...

Hello, If I am given a function of several variables and a parameter. Such as: f(x,y,z)=\frac{x y z^2}{(x^2+y^2+z^2)^k} This function is defined to be 0 where it is incontinuous (in (0,0,0)). How can I conclude for which values of k the function has three continuous partial derivatives? I...

I have been reviewing Calculus and have tripped up on figuring out to calculate the 2nd partial derivatives of imlicit functions. Kaplan and Spiegel give a cursory treatment to the subject in both of their "Advanced Calculus" books. Simply repeating the methods used to calculate the 1st...