Partial Definition and 1000 Threads

Homework Statement Write the chain rule for the following composition using a tree diagram: z =g(x,y) where x=x(r,theta) and y=y(r,theta). Write formulas for the partial derivatives dz/dr and dz/dtheta. Use them to answer: Find first partial derivatives of the function z=e^x+yx^2, in polar...

Homework Statement let w(u,v) = f(u) + g(v) u(x,t) = x - at v(x,t) = x + at show that: \frac{\partial ^{2}w}{\partial t^{2}} = a^{2}\frac{\partial ^{2}w}{\partial x^{2}} The Attempt at a Solution w(x-at, x+at) = f(x-at) + g(x+at) \frac{\partial }{\partial t}(\frac{\partial w}{\partial...

Homework Statement Let ##C## be a level curve of ##f## parametrized by t, so that C is given by ## x=u(t) ## and ##y = v(t)## Let ##w(t) = g(f(u(t), v(t))) ## Find the value of ##\frac{dw}{dt}## Homework Equations Level curves Level sets Topographic maps The Attempt at a Solution Is it true...

Homework Statement I'm currently in Calculus 3, and the professor gave us a "retro assignment" which is basically a bunch of tough integrals from Calculus 2. I think my process here is valid, but when I check my answer on Wolfram, they're getting a slightly different final answer...

Homework Statement Find the partial derivative of ## w = xe^\frac {y}{z} ##. Homework Equations N/A The Attempt at a Solution ## \frac{∂f}{∂x} = e^y/z ## ## \frac{∂f}{∂y} = \frac{xe^y/z}{z} ## ## \frac{∂f}{∂z} = (-yz^-2)(xe^yz^-1) ## Are theses correct? Thanks everyone.

Hi there, I have a a partial decay width in form of ## \frac{d \Gamma}{d \cos{\theta}~ dq^2} = ## some terms functions in q and ## \theta ## variables. How to integrate this decay width in Mathematica over this two variables ? I tried some thing like j[q_]:= ## \int_{1}^{-1} ## Gam[q, ##...

Hello guys, I have the system of PDE below and I want to solve it using finite difference method but I think I have to reduce it first to a system of first order PDE. The problem is that I don't know how to reduce this PDE to a first order system. I will appreciate any hints in this regard...

Homework Statement Find (∂z/∂x) of 6xyz Homework Equations N/a The Attempt at a Solution The correct answer is 6xy(∂z/∂x) but I would like proof of it. I got something different when I tried taking the partial derivative. 6xyz = 6x(yz) = Multiplication rule for derivatives 6(∂x/∂x) +...

Homework Statement integral(0>1) of (x^2+x)/(x^2+x+1)dx Homework Equations Factor denominator, and set numerator with A,B,C, etc. multiply both sides by the common denominator. The Attempt at a Solution Since the denominator won't factor at all I don't really know where to start, I could...

Homework Statement In considering the reaction: 3NO (g) + H2O (l) → 2HNO3 (aq) + NO (g) student A writes the equilibrium expression as: K=[NO][HNO3]2/[NO2]3 while student B writes: K=PNO [HNO3]2/[NO2]3 Whose equation is correct? Homework Equations NA The Attempt at a Solution This is a...

Hi, I'm using partial derivatives to calculate propagation of error. However, a bit rusty on my calculus. I'm trying to figure out the partial derivative with respect to L of the equation: 2pi*sqrt(L/g) (Yep, period of a pendulum). "g" is assumed to have no error. I know I can use the...

I've attached an image to this post. It essentially shows the equation for the first partial derivative using chain rule, which makes sense. What I'm confused with is how the second partial derivative was formulated. It seems they've simply squared the first partial derivative to find the second...

Homework Statement The rate constant for the conversion of methyl isonitrile is 5 x 10^-5. A scientist has a container containing this substance with a partial pressure of 100 torr. After 12.8 hours (46,000 seconds), what is the partial pressure of methyl isonitrile gas inside the container...

Homework Statement show that the following functions are differentiable everywhere and then also find f'(z) and f''(z). (a) f(z) = iz + 2 so f(z) = ix -y +2 then u(x,y) = 2-y, v(x,y) = x Homework Equations z=x+iy z=u(x,y) +iv(x,y) Cauchy-Riemann conditions says is differentiable everywhere...

Homework Statement x^2 + y^2 < 1 Find the partial derivatives of the function. Homework Equations x^2 + y^2 < 1 The Attempt at a Solution @f/@x = 2x = 0 @f/@y = 2y = 0 4. Their solution @f/@x = 2x = 0 @f/@y = 2y + 1 = 0 5. My Problem I don't see how / why they get 2y + 1 for the...

Homework Statement Homework Equations included in the first picture The Attempt at a Solution i feel confident in my answer to part "a". i pretty much just did what the u and v example at the top of the page did. but for part "b" i tried to distribute and collect like terms and what not...

When density functional theory is used to simulate a molecule adsorbed on a surface, it turns out that due to their interaction, a fraction of an electron is transferred from the surface to the molecule or vice versa. These interactions are normally categorised in interactions involving...

Homework Statement The problem statement can be expressed in one of these forms listed in order of preference. [/B] Every character with exception of x, y, t, and C are constants. Homework Equations I require a change of variable or series of subsequent change of variables that can convert...

Why, when a fraction has repeated linear terms in its denominator e.g. (11x2+14x+5)/[(x+1)2(2x+1)] does it have to be split into three partial fractions, A/(x+1) + B/(x+1)2 + C/(2x+1)? When my first saw this example, my initial reaction was to split it into A/(x+1)2 +B/(2x+1), but after working...

Homework Statement The problem and my attempt are attached Homework Equations Chain rule for partial differentiation perhaps And basic algebra The Attempt at a Solution I'm unsure of how to approach this but I differentiated all the expression at the top.

Homework Statement I want to find the partial derivatives in the point (0,0) of the function f:\mathbb R^2\rightarrow\mathbb R f(x,y):= \begin{cases} 0 & \text{if } (x,y) = (0,0) \\ \frac{y^5}{2x^4+y^4} & otherwise \end{cases} Homework Equations Our definition of the partial derivatives in...

Homework Statement The partial pressure of water vapor in air at 200 is 10[mm] mercury. according to the table of partial pressures we have to cool the air to 11.40 in order to bring the air to saturation, that is100% relative humidity. this according to the book. But when we cool the pressure...

Homework Statement take inverse laplace of: 6/[s^4(s-2)^2] Homework Equations 6/[s^4(s-2)^2] The Attempt at a Solution I used partial fractions. I was wondering if It could be manipulated to where I could use the laplace table?

Homework Statement A very long homogeneous cylinder is cut in half along its axis. One half s than equally heated, while the other half is equally cooled. How does the temperature change when the two parts are joined back together, if the cylinder is well isolated? Homework EquationsThe...

Homework Statement I have a PDE and I need to solve it in spherical domain: $$\frac{\partial F(r,t)}{\partial t}=\alpha \frac{1}{r^2} \frac{\partial}{\partial r} r^2 \frac{\partial F(r,t)}{\partial r} +g(r,t) $$ I have BC's: $$ \frac{\partial F}{\partial dr} = 0, r =0$$ $$ \frac{\partial...

What's the best approach to solving the partial-fraction decomposition of the following expression? $$\frac{1}{(a-y)(b-y)}$$ The expression is not of the following forms: But I know the solution is $$= \frac{1}{(a-b)(y-a)}-\frac{1}{(a-b)(y-b)}$$

Hey, Little confused by something: if we have u=x+y and v=xy what is the partial derivative w.r.t. u of y^2=uy-v I am told it is 2y (dy/du) = u (dy/du) + y And I can see where these terms come from. What I don't understand is why there is no (dv/du) term, as v and u aren't independent...

Homework Statement Find the specific solution for: y''-2y'+y=xe^x+4, y(0)=1, y'(0)=1. Homework Equations N/A The Attempt at a Solution Since xe^x is already in the general solution of the homogeneous version of this diff eq (complementary solution), my first guess for a partial solution...

Recently I started with multivariable calculus; where I have seen concepts like multivariable function, partial derivative, and so on. A week ago we saw the following concept: directional derivative. Ok, I know the math behind this as well as the way to compute the directional derivative through...

Homework Statement if z=\frac{1}{x^2+y^2-1} . Show that x \frac{\partial z}{\partial x} + y \frac{\partial z}{\partial y} = -2z(1+z) Homework Equations n/a The Attempt at a Solution I am extremely new to partial differentiation, I can get my head around questions where they just give...

Im doing a question on functionals and I have to use the Euler lagrange equation for a single function with a second derivative. My problem is I don't know how to evaluate \frac{d^2}{dx^2}(\frac{\partial F}{\partial y''}). Here y is a function of x, so y'=\frac{dy}{dx}. I know this is probably...

Homework Statement 2. The attempt at a solution By chain rule, which simpifies to, After this I am struck.

Homework Statement A voltaic cell utilises the following reaction: 4 Fe2+(aq) + O2(g) + 4 H+(aq) ---> 4 Fe3+(aq) + 2 H2O(l) What is the emf of this cell when [Fe2+] = 1.3 M, [Fe3+] = 0.010 M, PO2 = 0.51 bar and the pH of the solution in the cathode is 3.5. The standard reduction potentials...

Homework Statement If w = w(x, y, z) is given implicitly by F(x, y, z, w) = 0, find a formula for both ∂w/∂z and ∂^2w/∂y∂z . You may assume that each function is sufficiently differentiable and anything you divide by during the process of your solution is non-zero. The Attempt at a Solution I...

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.