Partial derivative Definition and 363 Threads

Homework Statement Question 2 from http://math.berkeley.edu/~mcivor/math53su11/solutions/hw6solution.pdf here. I do not understand b) and e). How do I think of the slope with respect to y? Homework Equations The Attempt at a Solution I do know that the partial derivatives are...

Greetings, In Griffiths E&M, 3rd. Ed., on page 214, the following is part of the derivation of the continuity equation (the same derivation is shown on the Wikipedia article for the current density, under the continuity equation section: http://en.wikipedia.org/wiki/Current_density)...

Hi everyone, Z=y+x^2*y+x^2+x^3+x^4+5 I would like to find the partial derivative of: diff(z,x) ? diff(z,y)? Kindly give me a step by step solution. Hope to hear from you soon. Thanking you all in advance for your replies.

Is \frac{∂y}{∂x}×\frac{∂x}{∂z}=-\frac{∂y}{∂z}?

Hi, I was reading something on conservative fields, in this example \phi is a scalar potential. (Please refer to the attatched thumbnail). It's partial derivatives, but I'm not sure why the d\phi/dx * dx, the dx should cancel out? and that should leave d\phi. So the integral should be -3∫d\phi...

Is partial derivative of ##u(x,y,z)## equals to \frac{\partial u}{\partial x}+\frac{\partial u}{\partial y}+\frac{\partial u}{\partial z} Is partial derivative of ##u(r,\theta,\phi)## in Spherical Coordinates equals to \frac{\partial u}{\partial r}+\frac{\partial u}{\partial...

Suppose I have some function f that depends on three variables, namely x, y, and t; i.e., f=f(x,y,t). Now suppose that y depends on x, i.e., y=y(x). Taking this into account, we see that f is really just a function of two independent variables, x and t. So my question is this: if I write down...

I've been studying a version of the finite element method. The author of a paper I was reading refers to the partial derivative of total elastic energy wrt position, partial derivative of surfacic energy wrt position, and partial derivative of strain wrt position. Does anyone know of a good...

Is there such a thing as a total "partial" derivative? Total Derivative as I've Been Taught From my understanding, if we have a function s = f(x, y) where the two arguments x and y are related by another function y = g(x), then there is a great deal of difference between ds/dx and ∂s/∂x. ∂s/∂x...

Hello, just a quick question about interpreting the partial derivative as a rate of change. My example is the area of a parallelogram: A = absinθ, with a and b being the adjecent sides with θ being the angle between them. We found the rate of change of the area A with respect to the side...

I don't understand the calculus behind this thermodynamics concept: S = f(T,P) dS = (∂S/∂T)_P*dT + (∂S/∂P)_T*dP (∂S/∂T)_V = (∂S/∂T)_P + (∂S/∂P)_T*(∂P/∂T)_V Basically, I don't get why and how you get (∂S/∂T) when you divide dS by dT. Also, I don't understand why the constant volume...

Hello, Could anyone please explain me the steps in these pictures. I do not understand the second step. http://imgur.com/AvVbPu5,Ust2Zpx#0 Second one: Third step ( i don't understand) http://imgur.com/AvVbPu5,Ust2Zpx#1 If anyone can give me detail explanation, i would really appreciate it.

Homework Statement If f is homogeneous of degree n, show that f_{x}(tx,ty)=t^{n-1}f_{x}(x,y). Homework Equations The Attempt at a Solution There are many solutions out there, and here's one of them: The proof is nice, but I just don't get it why from step 1 to step 2, \frac{\partial...

Hi all! I have the following slide, and whilst I understand that the original point is "the rate of density, ρ, in each volume element is equal to the mass flux"...i am totally lost on the mathematics! (And I am meant to be teaching this tomorrow). I do not have any information on what the...

Hi everyone, We just started learning partial derivatives and I understand the fx notation, but I'm confused when I'm asked for the value of fxy. Does this mean multiply the two derivatives together? For example: What is fxy when f(x,y) = (x+2y)ln(xy) Thanks!

Homework Statement Find df/dx, f(x,y)=integral of sqrt(1-t^3)dt from x^2 to x^3. Since it is asking to find the derivative with respect to x,should I regard t as a constant? Homework Equations The Attempt at a Solution I tried to find the antiderivative of the integral...

{\frac{∂(xy)}{∂x}=x} Going backwards. If we took, ∫x dy we get xy+f(x) Now, the only way that ∫x dy is a valid operation, is if we know that we came from a partial derivative. Why, when taking a partial...

Homework Statement Given the function f(x,y)=\frac{1}{2x^2 + y} Find the partial derivative fxx(x,y) Homework Equations The Attempt at a Solution Seems pretty straight forward, just treat y as a constant and differentiate twice. But I keep getting the answer wrong and I have...

When discussing the second partial derivative test in multivariate calculus, a reference is usually made to an elusive "higher order test" that one must defer to in the case that the second partial derivative test fails. Does anyone know the general form of these higher order test? My first...

How is the double derivative equal to that in the equation 2 in the attachment? =|

Homework Statement compute the gradient: ln(z / (sqrt(x^2-y^2)) Homework Equations ∇=(∂/(∂x)) + ... for y and z I just want to know how to do the first term with respect to x The Attempt at a Solution I am so rusty I don't know where to begin.

Homework Statement x3 + y3 + z3 - 3xyz = 6 Find (∂y/∂x)z. Homework Equations [b]3. The Attempt at a Solution [/ can i simply take the partial derivative of both sides treating z as constant? x3 + y3 + z3 - 3xyz - 6 = 0 f(x,y,z) = 0 (∂f/∂x)z = 0

I have a question to ask, is dx = δx, can they cancel each other like \frac{dx}{δx}=1 and is it mean that: \frac{δf}{δx}\frac{dx}{dt}=\frac{df}{dt}? (f = f (x,y,z))

Homework Statement Prove that if ##z=\arctan(\frac{xy}{\sqrt(1+x^2+y^2)})## , then: ##\frac{\partial^2 z}{\partial x \partial y}=\frac{1}{(1+x^2+y^2)^\frac{3}{2}} ## Homework Equations ##\frac{d}{d x} (\arctan(x)) = \frac{1}{1+x^2}## The Attempt at a Solution Differentiating z...

Homework Statement I'm trying to understand how a certain substitution can be made with regards to taking the partial derivative of a function product when the variable I am differentiating by is a function itself.Homework Equations (∂/∂p) (v(p)p(x,t)) = v(p) + (∂v/∂p)pThe Attempt at a...

Homework Statement Suppose f: R^2 --> R is differentiable and (df/dt) = c(df/dx) for some nonzero constant c. Prove that f(x, t) = h(x + ct) for some function h. Homework Equations hint: use (u, v) = (x, x+ct) The Attempt at a Solution df/dt = limk-->0 (f(x, x+ct+k) - f(x...

Homework Statement If u=f(x,y) where x=escost and y=essint show that d2u/dx2+d2u/dy2 = e-2s[d2u/ds2+d2u/dt2 Homework Equations http://s11.postimage.org/sjwt1wkvl/Untitled.jpg The Attempt at a Solution ok i don't understand how they got to that i don't know what d/ds is...

I have a question but have not seen an example or find anything in my textbooks so would love some advice on how to understand the problem. Its a theory question on partial derivatives of the second order... T=T(x,y,z,t) with x=x(t), y=y(t), z=z(t). Find the second derivative of T wrt t So...

I always see the example f(x,y)={xy/(x2+y2) if (x,y) =/= (0,0) and 0 if (x,y)=(0,0)} given as the example of a function where the partial derivatives exist at the origin but are not continuous there. I have a difficult time wrapping my head around this and was hoping someone could...

Hi all. I've recently started working a lot on my background in math and physics, since this year I began a new masters program which is quite math/physics heavy and I don't have a formal background in either field. I will try to get active on this forum, since I've been luring for some time and...

Evaluate partial derivative. chain rule?? I would like to represent the term identified in the image as (term 1) in terms of those partial derviatives that are known. Unfortunatly I just can't seem to wrap my head around it at the moment. :bugeye: A prod in the right direction would be...

the probability of finding particle is a constant with time <ψ|\partialψ/\partial(t)> = -<\partialψ/\partial(t)|ψ> , the equation holds for all ψ so the time derivative operator is an anti-hermitian operator, but then consider any hermitian operator A, the rate of change of A is d(<ψ|Aψ>)/dt =...

Any help would be much appreciated - Is it possible to say the following? If z = g(s+at) + f(s-at), let u = s+at and v=s-at, where a is a constant. z = g(u) + f(v), \frac{∂z}{∂u} = g'(u), \frac{∂^{2}z}{∂v∂u} = 0? or can ∂u and ∂v not even exist because it depends on two variables (a and...

Homework Statement Prove that (∂P/∂V) n,T = 1/(∂V/∂P) n,T n and T are supposed to mean that theyre just constants Homework Equations Ideal Gas PV=nRT The Attempt at a Solution I tried (∂P/∂V) n,T= ∂nRT/v/∂V = ∂nRT/V ∂V then I am stuck here

Homework Statement The problem is attached in the picture. The Attempt at a Solution I'm aware that: dU = T dS - P dV ∫ dU = ∫ (T) dS - ∫ P dV Are they assuming that T, P are constant so U = TS - PV ∂U/∂X = T (∂S/∂X) - P (∂V/∂X) Or is there a way to directly...

Hi! Here is my function: My task is to find: I think I know how to find ∂u/∂x, but I have no idea how to find ∂/∂z(∂u/∂x). Here is how I found ∂u/∂x: http://oi48.tinypic.com/prsly.jpg Does someone know how to find ∂/∂z(∂u/∂x)? I appreciate any help :)

Homework Statement The changing variable formula in partial derivative f(u,v) x=x(u,v) y=y(u,v) (∂f/∂x)y = (∂f/∂u)v(∂u/∂x)y + (∂f/∂v)u(∂v/∂x)y I khow the how chain rule works, but I don't know why in the (∂f/∂u) v is constant and in the (∂u/∂x) y is constant Homework Equations The...

Homework Statement In the first paragraph, I know its missing a function which they did not put, g. Without puting ∂g/∂x but simply putting ∂/∂x, is that equation even mathematically correct? I know they are "filling in the g later" but does this corrupt the in-between steps in anyway? In the...

Homework Statement Hey, i ve got problem with a few partial derivative problems. 1.I have a function T(x,t) Prove that dT/dt=∂T/∂t +∂T/∂x dx/dt 2.Let u(x,y) and y(x,u) be continous, differentiable functions. Prove that ∂u/∂z=∂u/∂z ∂y/∂z 3 Let r(q1,q2,...qn) be a function of place...

Homework Statement What does it mean when lowercase Delta (δ) is used in partial derivative and derivative notation? Does it make any difference? Or is it just a personal preference? Homework Equations - The Attempt at a Solution Google

I am having trouble finding the rule for the (partial) derivative of an expression like y = f(X)^{g(X)} can anyone help?

Could someone please explain to me how to find the derivative of this: dy/dx = φ(x, y) Should I break up the equation to make it dy/dx = φ(x) + φ(y) and then derive the parts? I would then get d²y/dx² = ∂φ/∂x + ∂φ/∂y do I have to also multiply both terms by their respective derivatives...

For some non-linear 3D function, let's say I want to take the partial derivative for x where y is constant. Each point for Z will be different of course since it's non-linear. So let's say I plug in an X of 3 where Y is constant for some function and I get a slope of 5 as my answer. Is it...

So I have a proof and I can't follow the process, I think its because I haven't learned how to do partial derivatives or I've forgotten, anyways can someone tell me if this is a rule in calculus (∂Cv/∂V)T=0 I've gotten to [(∂/∂V)(∂U/∂T)V]T and the proof I have goes to...

Homework Statement If f(x,y) = x(x^2+y^2)^(-3/2)*e^(sin(x^2y)) find the derivative of f with respect to x at the point (1,0). The Attempt at a Solution The textbook solution just plugs 0 into y and gets f(x) = x^-2 and then proceeds to differentiate this resulting in the answer -2. I...

Homework Statement The electric potential in a certain region of space is given by: V(x,y,z) = 1000x-2000y-1500z(Volts). a.)Find the electric field corresponding to the given electric potential. Draw some electric field lines. b.) What charge distribution can create this electric field? Give...

Hi, I find my professor doing this a lot of times, here is it: ∫{ ∂(f[x])/∂x } dx = ∫d(f[x]) How is that possible?

Homework Statement Given 4 state variables x, y, z and w such that F(x,y,z)=0 and w depends on 2 of the other variables, show the following relations: 1)\left ( \frac{\partial x }{\partial y } \right ) _z = \frac{1}{\left ( \frac{\partial y }{\partial x } \right ) _z} 2)\left (...

Homework Statement w = 2xy + 4yz + 5xz x = st y = 3^(st) z = t^2 s=5 t=1 Homework Equations Chain rule: xy = x*y' + y*x' The Attempt at a Solution w = 2stest + 4test + 5st3 (partial derivatives) dw/dt = 2s2test + 2sest + 4tsst + 4est + 15st2 (partial derivatives) dw/dt (5,1) = 2(5)2e5 +...

Homework Statement The question is attached as Question.jpg. Homework Equations Partial differentiation. The Attempt at a Solution This seems obvious to me but I don't know how to express myself mathematically. Basically, what I'd do is: [∂(u,v)/∂(x,y)] [∂(x,y)/∂(r,s)] =...