Partial Definition and 1000 Threads

Homework Statement Find the partial derivative of a*cos(xy)-y*sin(xy) with respect to y. Homework Equations None. The Attempt at a Solution The answer is -ax*sin(xy)-sin(xy)-xy*cos(xy). I know that I need to treat x as constant since I need to take the partial derivative with respect to y...

\mathcal{L}_M(g_{kn}) = -\frac{1}{4\mu{0}}g_{kj} g_{nl} F^{kn} F^{jl} \\ \frac{\partial{\mathcal{L}_M}}{\partial{g_{kn}}}=-\frac{1}{4\mu_0}F^{pq}F^{jl} \frac{\partial}{\partial{g_{kn}}}(g_{pj}g_{ql})=+\frac{1}{4\mu_0} F^{pq} F^{lj} 2 \delta^k_p \delta^n_j g_{ql} I need to know how...

I'm trying to come up with an expression for \partial y / \partial x where z = f(x,y). By observation (i.e. evaluating several sample functions), the following appears to be true: \begin{equation*} \frac{\partial z}{\partial x} + \frac{\partial z}{\partial y} \cdot \frac{\partial y}{\partial...

I saw it yesterday. I live in the Pacific Northwest, which was clouded over. But at about 2:45 - 3:00 PM PDT, at local maximum eclipse, there was a break in the lower clouds, and I could see the Sun through the upper clouds. It was rather fuzzy-looking, but I could see a bite out of it from the...

Hello, we haven't really covered partial differentiation in my maths course yet, but it has come up a few times in mechanics where the 'grad' operator is being introduced, so I'm trying to learn about it myself. I'm looking at the partial derivatives section in "Mathematical Methods In The...

I am quite new to the topic of multivariable calculus. I came across the concept of "gradient" (∇), and although the treatment was somewhat slapdash, I think I got the hang of it. Consider the following case: ##z = f(x,y,t)## ##∇z = \frac{∂z}{∂t} + \frac{∂z}{∂y} + \frac{∂z}{∂x}## If we're...

1. x^2-x+1 Is this factorable? My initial thinking is NO. However, I can complete the square and it becomes (x-1/2)^2-3/4, but this doesn't seem to help me. Would this be considered factorable? 2. Turn 1/x^2-x+1 into partial fractions Clearly, after I answer #1 correctly, #2 will be more...

Homework Statement This is actually an electromagnetism problem but all the physics is done, I just don't remember how to solve the PDE: \frac{d^2V}{dr^2}=-\frac{2}{r}\frac{dV}{dr} The d's should be del's, just don't know how to do that... Homework Equations Not sure. The Attempt at a...

Hi Physics Forums, The solubility of a gas according to Henry's Law depends on partial pressure. Would an increase in pressure in a system increase the solubility of a specific gas, even if the partial pressure of that particular gas doesn't change? The system described above increases in...

Homework Statement Find \frac{\partial f}{\partial x} if f(x,y)=\cos(\frac{x}{y}) and y=sinx Homework Equations See above The Attempt at a Solution For \frac{\partial f}{\partial x} I calculated -\frac{1}{y}\sin(\frac{x}{y}) which comes out as \frac{-\sin(\frac{x}{\sin(x)})}{sinx} and this...

x^2 - y^2 +2mn +15 =0 x + 2xy - m^2 + n^2 -10 =0 The Question is: Show that del m/ del x = [m(1+2y) -2 x n ] / 2 (m^2 +n^2) del m / del y = [x m+ n y] / (m^2 +n^2) note that del= partial derivativesMy effort on solving this question is Fx1=2x Fm1=2n Fx2 =2y Fm2 =-2m del m /del x =...

Homework Statement Problem 29. Use the subtraction trick U(tilda) = U−U1 to reduce the following problems with non-canonical boundary conditions to the canonical ones and write down the equations in terms of the variable ˜u (do not solve them). Note that there are infinitely many u1’s that...

Homework Statement Given the functions Q(v,w) and R(v,w) [/B] K = v(dQ/dv)r and L = v(dQ/dv)w Show that (1/v)K = (1/v)L + (dQ/dw)v (dW/dv)r I have the problem attached if for clarity of the information. Homework Equations I assume everything is given in the problem. The Attempt at...

I have a difference of opinion with 2 calculation engines. equation to solve is; d/dx (a(x^2 +y) Wolframalpha of course is a very trusted source but I also use symbolab. Here is a screenshot of the differential I want from both sites and associated answers. . . . and the wolfram solution...

Hello PF! It's been a while since I last posted here. I have come across a problem in my textbook, which asks me to find expressions for V as a function of T and P, starting from the coefficients of thermal expansion and compressibility. \alpha = \frac{1}{V} \left(\frac{\partial V}{\partial T}...

please help decompose$\frac{4x^2y}{(x^2-2xy+2y^2)(x^2+2xy+2y^2)}$ I've used the cases I know for this problem but to no avail. please help me.

How do I go about solving a differential equation of the form \partial_{x}F_{x}(x,y) + \partial_{y}F_{y}(x,y) = g(x,y) Where g(x,y) is a known function and I wish to solve for F. I thought i could apply the method of characteristics but the characteristic equation is dependent on coefficients...

Hi I need help regarding following can I write following partial derivative wrt x multiplied by Ax (∂A[x])Ax =∂(Ax^2)

[b] Homework Equations N/a The Attempt at a Solution I am wondering if this is the right direction in solving this. any input would be great! Sorry for the messy handwriting!

Hi all , I would like to solve the following partial differential equation. (∂α/∂t)=G[sub(α)] *(a'-a) I attached the equation and solution here as an image. I don't know how it was derived. I hope someone can help me

Homework Statement To find the decomposition of a polynomial with a repeated factor in the denominator, you should separate them into (x+a)^1 + ... + (x+a)^n. But, my question is why? For example, why should you decompose it in the following way: \frac{x+2}{(x+1)(x+3)^2} = \frac{A}{x+1}...

Homework Statement Find (\frac{dV}{dp})_{n,T} for the Van de Waals gas law Homework Equations Van de Waals gas law: (\frac{p+an^2}{V^2})(V-nb)=nRT The Attempt at a Solution I just started doing problems like these so I would like to know if I am doing them right... What I did was I took...

Hi. Assume there's a probability ##q## for a guy to take a step to the right, and ##p=1-q## to take one to the left. Then the probability to take ##n## steps to the right out of ##N## trials is ##P(n) = {{N}\choose{n} }q^n p^{N-n}##. Now, what is ##<n>##? My textbook in statistical physics...

Please help me with this, In Reheat Rankine cycle, we first Expand the steam partially in a high pressure turbine and then reheat it again . How is this partial expansion in high pressure turbine done ? in the sense, what is the procedure followed to have only partial expansion of steam...

can anyone tell me the difference of application of total derivative and partial derivative in physics? i still can't figure it out after searching on the internet

many books only tell the operation of total derivative and partial derivative, so i now confuse the application of these two. when doing problem, when should i use total derivative and when should i use partial derivative. such a difference is detrimental when doing Physics problem, so i...

1. Gaseous compound Q contains only xenon and oxygen. When 0.100 g of Q is placed in a 50.0 mL steel vessel at 0 °C, the pressure is 0.229 atm. When the vessel and its contents are warmed to 100 °C, Q decomposes into its constituent elements. What is the total pressure, and what are the partial...

Homework Statement Doing a homework question and I ran it through wolfram and I get a different answer to what I'm working it out as...and I can't see where I'm going wrong. Anyone able to give a pointer? my equation is \frac{1}{s(0.641s + 1)} Wolfram gives the answer as...

I always see people when doing partial fraction decomposition just plug in arbitrary values of x to cancel out some constant terms like A,B,C in order to solve it. I just want to know how this works. I've heard that since A,B, and C are constants it has to hold true for any values of x(like a...

Homework Statement H2(g) + S(s) = H2S(g) Kc= 6.8x10^-2 If 0.2 moles of H2 and 1.0 mole of S are heated in a 1L vessel upto 90C, what will be the partial pressure of H2S at equilibrium? Can someone help me with this step by step?Homework Equations The Attempt at a Solution Kc = 6.8X10^-2 = x /...

Homework Statement Given f(x, y, z) = 0, find the formula for (\frac{\partial y}{\partial x})_z Homework Equations Given a function f(x, y, z), the differential of f is df = \frac{\partial f}{\partial x}dx + \frac{\partial f}{\partial y}dy + \frac{\partial f}{\partial z}dz...

Homework Statement If xs^2 + yt^2 = 1 and x^2s + y^2t = xy - 4 , find \frac{\partial x}{\partial s}, \frac{\partial x}{\partial t}, \frac{\partial y}{\partial s}, \frac{\partial y}{\partial t} , at (x, y, s, t) = (1, -3, 2, -1) Homework Equations The Attempt at a Solution I...

Alright, I am here again with another question... When I have a rational function, let's say (x+4)/(x-2)(x-3) I rewrite it like A/(x-2) + B(x-3) and then solve it for A & B. But when we have for e.g (x^2 + 3x + 2)/(x(x^2 +1 )) the book tells me to rewrite it like: A/x + (Bx + C)/(x^2 + 1)...

Homework Statement On a planet not entirely unlike earth, the ratio of the partial pressure of N2 to that of O2 equals 1 at an altitude of 1 km: \frac{p_{\text{N}_2}}{p_{\text{O}_2}} = 1. Assuming that T = 200 K, and the gravitational constant is 5 m/s2, what is the ratio...

Homework Statement The problem and solution are attached as TheProblemAndSolution.jpg. I will also copy down the problem and solution here.: Problem: Consider the set ℤ of integers. Define aRb by b = a^r for some positive integer r. Show that R is a partial order on ℤ, that is, show that...

\int \frac{7dx}{x(x^2+8)^2} so I am thinking its going to be set up like: \frac{A}{x} + \frac{Bx + C}{x^2 + 8} + \frac{Dx + E}{(x^2 + 8)^2} Practice problem I'm stuck on. so I cleared fractions and got A = 7/64 , b = -7/64 and C = 105/64 and now I'm lost... can anyone work this problem for me...

Homework Statement Find the partial fractions for this expression. (((n+1)*(sqrt(n)) - n*(sqrt(n+1))) / (n*(n+1))) The Attempt at a Solution The final answer is 1/sqrt(n) - 1/(sqrt(n+1)) My work: A/n - B/(n+1) = n*sqrt(n+1) - (n+1)*(sqrt(n)) I am subbing in n = -1 and n = 0 to solve for...

Without being too concerned how we got there. The answer to a partial fraction question a friend and I are doing is 24/5 ln(2) - 8/5ln(3) The system does not accept this answer however, it wants the simplified form 8/5 ln (8/3) We're not sure how to get that form. More specifically 8/5...

I'm a little rusty with partial fractions, and I can't seem to find my error once I get up to that point. Homework Statement dy/dx = (y^2 - 1) / x Homework Equations The Attempt at a Solution Cross-mutliply x dy = (y^2 - 1) dx Divide by the appropriate terms dy / (y^2...

Hey guys, Here is another pair of questions that I'm doubting at the moment: I used partial fractions for A and got (Bx+C)/x^2 + Ax/(x-1)^2 + Dx(x-1) which led me to compute A=1, B=0, C= -1, and D=0, which already sounds off. Do you guys have any suggestions? Also, for 5b, I calculated B=...

Homework Statement Evaluate the integral. (Remember to use ln |u| where appropriate. Use C for the constant of integration.) \int \frac {5x^2 - 20x +45}{(2x+1)(x-2)^2}\, dx Homework Equations 5x^2 - 20x +45 = 5 (x^2 -4x +9) The Attempt at a Solution I'm able to come up with an...

First the example problem. This is an integral of the whole thing (3x^3+24x^2+56x-5) / (x^2+8x+17)^2 The answer comes out to be 3/2 ln(x^2+8x+17) - (49/2 tan^-1(x+4)) - (25x+105 / 2(x^2+8x+17) + C I would show all the steps but I'm still not sure on how to use the format tools, so that...

I just need some clarification that this is fine so I have f_{x} = -2xe^{-x^2-y^2}cos(xy) -ysin(xy)e^{-x^2-y^2} now, taking the second derivative f_{xx} = [-2xe^{-x^2-y^2}+4x^2e^{-x^2-y^2}]cos(xy) - ysin(xy)[-2xe^{-x^2-y^2}]+2xe^{-x^2-y^2}sin(xy)y-cos(xy)e^{-x2-y^2}y^2

I know how to prove this via limits and I'm okay with that. What I want to understand is the interpretation of the theorem and specifically a visualisation of why what the theorem states must be the case. My guess is that this theorem is saying that change is symmetrical. But I don't know...

Hey guys, I'd really appreciate it if I could get some quick help for this problem set I'm working on. For question one, I just did a quick u substitution for x^4 and managed to get x^4 * sin(x^4)+cos(x^4) + C. For part b, I used integration by parts and took ln(4t) as u and the rest as...

There is a device called a Fizz Keeper that attaches to carbonated beverage bottles and is supposed to keep them from going flat after they are opened by pressurizing them with air. Dalton's law and Henry's law have been used to debunk the device as ineffective. The argument against the...

1. Marine biologists have determined that when a shark detects the presence of blood in the water, it will swim in the direction in which the concentration of the blood increases most rapidly. Suppose that in a certain case, the concentration of blood at a point P(x; y) on the surface of the...

Let's say we have a function F(\vec{r})=F(s, \phi, z). Then (correct me if I'm wrong): \frac{dF}{dx}=\frac{\partial F}{\partial s}\frac{ds}{dx}+... So then what is \frac{\partial F}{\partial x}? Is it zero because F doesn't depend explicitly on x? Is it the same as \frac{dF}{dx}=\frac{\partial...

Find the partial fraction decomposition for the rational function. \frac{-4x^2 - 8x - 19}{(x^2 + 2)(x-9)} I'm not sure what to do.

Hello! This is my first post to this excellent forum! I would like some help with this exercise: u_{xx} (x,y) + u_{yy} (x,y) = 0, with 0 < x < 2 \pi , 0 < y < 4 \pi u_x (0,y) = 0, \, u_x(2 \pi, y) = 0, \, 0< y < 4 \pi u(x,0) = a \cos(2x), \, u(x, 4 \pi) = a \cos^3(x), \, 0<x<2\pi...