Derivatives Definition and 1000 Threads

Homework Statement Suppose that z=f(ax+by), where a and b are constants. Show that bz(x) = az(y). z(x) means partial derivative of z with respect to x, as for z(y). Homework Equations The Attempt at a Solution Say z=ax+by z(x) = a z(y) = b So bz(x) = ba = ab = az(y)...

[x_{\alpha}, p_{\alpha}]\psi(r)=[x_{\alpha}(-i\hbar \frac{\partial}{{ \partial x_\alpha}})-(-i\hbar\frac{\partial}{\partial x_{\alpha}})x_{\alpha}]\psi(r) why the result is i\hbar\psi(r) should not be 0? and then the same situation why in this case we get 0? [x_{\beta}...

Homework Statement Well, let's take F: x^2 y^3=0 . Now, let's say thay y=y(x), y being an implicit function of x. I want to find 2nd row derivative \frac{d^2y}{dx^2} using differential operator. Homework Equations not apply The Attempt at a Solution Using D for the first...

Homework Statement Find the constants A and B such that the function y = Asinx + Bcosx satisfies the differential equation y'' + y' - 2y = sinx Homework Equations None The Attempt at a Solution My attempt: y = Asin x + Bcosx y' = Acosx - Bsinx y'' = - Asin x - Bcosx y''...

Homework Statement I have a few problems that are giving me some trouble: 1. Take the derivative of xe-4x 2. Find dy/dx and evaluate the slope for the curve ey^3 - 2x4 + y2 = 3 at (8,0) 3. Find dy/dx and evaluate the slope for the curve e-y - 4 = x2 + 1 at (-2,2) Homework Equations N/A...

Hi everyone! I'm new to online math forums. I wonder if anyone can give me a hand on this - it would be greatly appreciated. Thank you in advance! Dave Homework Statement If a box with a square base and an open top is to have a volume of 160 cubic feet, find the dimensions of the box having...

Hello, How is Taking the derivative on the top and bottom makes it go in circles Thank you

Do I need to use Schwarz's or Young's theorems to prove it, if don't then do I need to evaluate them on (0,0) using definition.

According to the statement(attached file) in order to find the directional derivative I must know unit vector along the direction and the point at which to find the directional derivatives. From the angle I can find out the direction (as the cosine of the angle) but not the point. Then how can I...

Homework Statement Prove (∂V/∂T)_s/(∂V/∂T)_p = 1/1-(gamma) (gamma = Cp/Cv) Homework Equations (∂V/∂T)_s = -C_v (kappa)/(beta)T (where beta = 1/V(∂V/∂T)_p, kappa = -1/V(∂V/∂P)_T C_v= - T(∂P/∂T)_v(∂V/∂T)_s The Attempt at a Solution As part(a) ask me to find C_v, I do it similar for...

Homework Statement Suppose the differentiable function f(x,y,z) has the partial derivatives fx(1,0,1) = 4, fy(1,0,1) = 1 and fz(1,0,1) = 0. Find g'(0) if g(t) = f(t2 + 1, t2-t, t+1).Homework Equations The Attempt at a Solution Ok I'm given the solution for this and I'm trying to work through it...

Hey guys, any hints on how to show that \frac{d}{dt}|t=0 det(I + tA) = tr(A) ? I did it for 2x2 but I can't figure out a generalization. Thanks

Homework Statement For the function f(x)=(x^2-3)/(x-2), determine the locations of any points of inflection, if any

Homework Statement Given Homework Equations The Attempt at a Solution

how can i find a power series representaion of d/dx (1/x-9)

I've been trying to get a grasp on Lie Derivatives. I understand that we can represent a lie derivative acting on a vector as a commutator. What do I do when I act a lie derivative on a tensor? Can I still just write out the commutator?

Homework Statement I am translating the question from another language so it might not be word to word with the original question. assume x(s,t) and y(s,t) determined by these two functions: sin(xt) +x+s=1 eyt+y(s+1)=1 The following function is defined H(x,y)=x2+y2-xy such that...

Hi, I am incredibly confused about second derivatives of the metric. I know that in general, the covariant derivative of a vector is given by \nabla_a v^b = \partial_a v^b + \Gamma^b_{ac}v^c and I think I understand how to generalize to higher rank tensors (just decompose into an...

If I have u = u(x,y) and let (r, t) be polar coordinates, then expressing u_x and u_y in terms of u_r and u_t could be done with a system of linear equations in u_x and u_y? I get: u_r = u_x * x_r + u_y * y_r u_t = u_x * x_t + u_y * y_t is this the right direction? Because by...

Hi, so I'm trying to solve Laplace's equation by separation of variables, and there's a basic step I'm not understanding with regards to the product rule. Given A product rule (i think) is taken to make the first term easier to deal with and we get I'm just having trouble...

Homework Statement Compute the 6th derivative of f(x) = arctan((x^2)/4) at x = 0. Hint: Use the Maclaurin series for f(x). Homework Equations The maclaurin series of arctanx which is ((-1)^n)*x^(2n+1)/2n+1 The Attempt at a Solution I subbed in x^2/4 for x into the maclaurin...

Homework Statement I'm in Pre-Calculus this semester and it's going swimmingly and I thought I'd try and get ahead for Calc I, which I plan on taking this summer. Anyways, all I have really to go off of right now is "How to Ace Calculus: The Streetwise Guide", my brain, and wikipedia. I'm...

hints? Derivatives: Intervals, stationary points, logarithms, continuous functions Homework Statement Got any hints or anything? 1. Suppose that f(x) = (x - 3)^4 ( 2x + 5)^5 a) Find and simplify f ' ( x ) b) Find stationary points of f c) Find exactly the intervals where f is...

Homework Statement The cost in dollars for producing x units is given by C(x) = 1.22x+ 2500 . The demand curve is given by p(x) = (60,000-x)/(10,000) A. Find the revenue function R(x) in simplest form. B. Find the marginal revenue function and the marginal revenue for selling 15000...

Homework Statement Sorry about not using the template, but I didn't really see how I could have. If you guys/gals could please check over my answers to these questions and point out the ones I miss that would be outstanding. Thank you! 1. The position of an object moving on a coordinate...

I am still working on getting anything other than subscripts to post with my latex formatting, so for now I have posted a word document. Any help would be greatly appreciated, thanks. Joe

Homework Statement Let f(x) be a twice differentiable function on an interval I. Let f''(x)>0 for all x in I and let f'(c)=0 for some c in I. Prove f(x) is greater than or equal to f(c) for all x in I. Homework Equations Mean value theorem? The Attempt at a Solution f''(x)>0...

What is Cusp and what are the values of derivatives on left and right side of it?

What is de real difference between parcial and total time derivatives of kets?

I have some data in a text file. I want to import this data into Mathematica, and then I want to calculate the numerical derivatives of this data. In particular, I need to find the y value where the first derivative is equal to zero. I can import data. I can use the ND function for numerical...

Homework Statement I have often heard that given say, ds/dt=k, that it is not entirely rigorous to say that ds=kdt. Why is that? If I view the derivative as nothing more than a ratio of the differentials, that seems perfectly reasonable. Also I see this done all the time, with acknowledgment...

Homework Statement Solve the differential equation: dy/dx=(y-y2)/x , for all x\neq 0 Homework Equations Integration by Parts: \int u dv = u v - \int v du \intlnx= 1/x + C \int (1/x) = lnx + C dy/dx lnx = 1/x dy/dx 1/x = lnx The Attempt at a Solution dy/(y-y2)=dx/x \int...

The problem statement. Suppose x''(t) = 1 for 1\leq(t)\leq2, and x''(t) = 0 for all other (t) (a) Plot x''(t) for 0\leq(t)\leq3 (b) Plot x'(t) for 0\leq(t)\leq3. Assume x'(0) = 0 (c) Plot x(t) for 0\leq(t)\leq3. Assume x(0) = 0The attempt at a solution I assumed 'x' being the vertical axis...

Homework Statement Given Cartesian coordinates x, y, and polar coordinates r, phi, such that r=\sqrt{x^2+y^2}, \phi = atan(x/y) or x=r sin(\phi), y=r cos(\phi) (yes, phi is defined differently then you're used to) I need to find \frac{d\phi}{dr} in terms of \frac{dy}{dx} Homework...

Homework Statement A mapping f from an open subset S of Rn into Rm is called smooth if it has continuous partial derivatives of all orders. However, when the domain S is not open one cannot usually speak of partial derivatives. Why? Homework EquationsThe Attempt at a Solution In the 1...

nvm got it

Hello, I should feel ashamed to ask this, but it's giving me (and others) some troubles. given f(x_1,\ldots,x_n), is it wrong to say that: \frac{\partial f}{\partial f}=1 ...?

In the Wolfram Mathworld section on spherical coordinates there's given a list of nine covariant derivatives. The derivatives are given with respect to radius, azmuth, and zenith using the usual symbols r, theta and phi. The question is: what would be examples of the vectors whose derivatives...

Homework Statement I don't understand why they took M(e)=1 , and how the proceed on with the proof. Thanks in advance(= Homework Equations The Attempt at a Solution

How do I show that a Vector field X on \Re^{3} is tangent to a Cylinder in \Re^{3}?

Hi all, I'm looking at the following problem: Suppose that f:\mathbb{R}^2\to\mathbb{R} is such that \frac{\partial{f}}{\partial{x}} is continuous in some open ball around (a,b) and \frac{\partial{f}}{\partial{y}} exists at (a,b): show f is differentiable at (a,b). Now I know that if both...

I've seen derivatives and integrals used before to change the form of an equation to one that is more suitable for solving a problem. Usually the person will just differentiate both sides and the equality holds? Is this always the case? Because if you take the derivative of both sides of x^2...

Homework Statement y = \log_{2}(x^2 + 1) Homework Equations I think the pattern is: \frac{d}{dx}[\log_{b}(x)] = \frac{1}{x ln(b)}The Attempt at a Solution y\prime = \frac{2x}{(x^2+1)ln(2)} I did this by applying the pattern (that may or may not be correct) and then chain ruling the...

Homework Statement Find the point on 2x + 3y + z - 11 = 0 for which 4x^2 +y^2 +z^2 is a minimum Homework Equations The Attempt at a Solution Using lagrange multipliers I find: F = 4x^2 + y^2 + z^2 + l(2x + 3y + z) Finding the partial derivatives I get the three equations...

f(x) = 2^x \left \left f(kx) = 2^(kx) \left \left b = 2^k \left \left b^x = 2^(kx) \left \left b^x = f(kx) \frac{d}{dx}(b^x) = \frac{d}{dx}(f(kx)) = \frac{d}{dx}(2^(kx)) (1) \frac{d}{dx}(f(kx)) = k.f'(kx) (2) I can't see how step (1) gets to step (2). Because I thought...

Homework Statement Two sides of a triangle have lengths a and b, and the angle between them is theta. What value of theta will maximize the triangle's area? (Hint: A=1/2absin(theta) The Attempt at a Solution I have a triangle drawn, with the base being a, and the height being b...

I'm searching for a function expressed explicitly as a non-infinite series where f(0)=1/1 f'(0)=1/3 f''(0)=1/5 ... fn(0)=1/(2n+1) ... Does it exist? What is it?

In differential geometry what does df mean as in \mbox{f} : \mathbb{R}^m \mbox{ to } \mathbb{R}^n Then df is what? the jacobian matrix of partial derivatives?

Homework Statement find the dy/dx of y= 4- x (to the 2nd power) sin x Homework Equations is there a rule? The Attempt at a Solution nothing

I am confused about how to find arctan and arcsin Specific Problem: y= arctan(4x/7) find derivative with respect to y I know that d/dx arctan is 1/(1+x^2) am stuck on what to do. Any help would be awesome thanks!*p.s. i am very new to this site and it looks awesome! also not exactly sure...