Partial derivatives Definition and 417 Threads

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...