Partial derivatives Definition and 435 Threads

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...

hello, i am supposed to use the two variable chain rule to confirm that changing variables from (x,y) to (v,w) with v=x and w=y/x leads to: \partial{v}=\partial{x} + w\partial{y} and \partial{w}=x\partial{y} it seems to me that the first line should read \partial{v}=\partial{x} =...

Hey, I have no idea where to start, for this question. I know that I will probably have to use vector and scalar product and use the trig identity tan^2(theta)=sec^2(theta)-1 - and of course partial derivatives Question: In order to determine the angle theta which a sloping plane ceiling...

Hey, I have no idea where to start, for this question. I know that I will probably have to use vector and scalar product and use the trig identity tan^2(theta)=sec^2(theta)-1. Question: In order to determine the angle theta which a sloping plane ceiling makes with the horizontal floor...

On MathWorld's site, they said that (\frac{\partial{y}}{\partial{x}}){_f} = -\frac{(\frac{\partial{f}}{\partial{x}})_{y}}{(\frac{\partial{f}}{\partial{y}})_{x}} So can this method be used instead of implicit differentiation? Will I get the same result? This seems kind of like a...

I'm given F(x*y;z/x), where z=z(x,y). I have to proof that (∂z/∂x)*x+(∂z/∂y)*y=3*z I have expressed all partial derivatives, but I got only (∂z/∂x)*x-(∂z/∂y)*y=z I think that it's impossible at all to solve this problem, because z is arbitrary function as i understand. Help me please. Where...

i am trying to solve the following problem: find the limit of (xy)/((x^2)+(y^2))^(1/2) as (x,y) approaches (0,0). i know it's kind of hard to read, but that is xy divided by root(x-squared + y-squared). the area where i am having a problem is in my arithmatic. how do i multiply the...

For a function, z = f(x, y) \frac{\partial z}{\partial x} = \lim_{\delta x\rightarrow0} \frac{f(x +\delta x, y) - f(x, y)}{\delta x} \frac{\partial z}{\partial y} = \lim_{\delta y\rightarrow0} \frac{f(x, y+\delta y) - f(x, y)}{\delta y} What is partial increament \delta x, \delta y ...

I am sort of skipping around at my own pace in Courant's Calculus book and came across partial derivatives. Are they geometrically the intersection of a plane and a surface? Why do we keep only one variable changing and the other variables fixed? Is it basically the definition of the derivative...

Original question: Let w = y^2 + xz. If x = rcos(theta), y = rsin(theta), and z = z, find (partial w)/(partial r) and (partial w)/(partial theta). Could someone please check my answers? (partial w)/(partial r) = zcos(theta) + 2ysin(theta) (partial w)/(partial theta) = -rzsin(theta)...

Let \vec{r} = \vec{r}(q_1,\ldots,q_n) . Is the following ALWAYS true? \frac{\partial \vec{r}}{\partial q_i} \cdot \frac{\partial \vec{r}}{\partial q_j} = \delta_{ij} Edit: Perhaps I should ask if it is zero when i \neq j rather than saying that it is 1 when i = j I guess...

Is there some underlying difference between the two types of derivatives?Other than the obvious that one is used on single variable functions, while the other is for multivariable functions. I'm asking because my classical professor mentioned something about knowing the difference between the...

Partial Derivatives of this(respect to x,y). Z = (x+y) Sec(xy). Would my first move be to multiply the (x+y) tot he other side? If so I'm algerba is a bit sketchy :rolleyes: , how would it be done.

Given a scalar-valued function f=f(x,y), if it's true that \frac{\partial^2 f}{\partial x \partial y}=\frac{\partial^2 f}{\partial y \partial x}, what does that tell about function f? Does it mean that it's continuous, or does it need to be smooth, or...?

ok i need help with a few questions. i'll post the question first and then what i get as an answer, the first one is the partial derivative with respect to x and the second one with respect to y. these are the even number questions from my textbook and they don't have answers to them so if...

We were gievn a question in tutorial last week asking us to calculate the Taylor series of the function f(x,y) = e^(x^(2) + y^(2)) to second order in h and k about the point x=0, y=0 I've got the forumla here with all the h's and k's in it and have it written down, but it's actually how to...

I am having a hard time doing the following problems. First off all the notation is confusing the hell out of me. This is the first time i have used this notation so it is making learning very difficult. Here are my questions. Prove the following function is differentiable, and find the...

here there are Exercises on Partial Derivatives: http://www.uAlberta.ca/dept/math/gauss/fcm/calculus/multvrbl/basic/partl_drvtvs_exrcss/partl_dervtv_exrcss.htm can comeone please solve the first two problems (for some reason i can't read the answers). my answers: 1. 3(3xy-4y^2)^2(3x-8y) 2...