Derivatives Definition and 1000 Threads

Homework Statement I want to show that the partials exist for a certain function. Homework Equations My book says that if a function f is differentiable at a point x then the partial derivatives exist. The Attempt at a Solution Rather than showing f is differentiable, I am...

I just ran into this problem and have no idea how to solve it. Basically I'm trying to prove that all orders of derivative of the given function is bounded by the function on the right. I'm pretty sure the inequality is true, but I really have no clue on how to prove it. I thought about using...

In this textbook, how exactly are 2.2.19 and 2.3.21 equal? http://i.imgur.com/LrcXE.png

Homework Statement In one of my class's tests I've come across the following equation: \frac{d^2 y}{dx^2} \: + \: \left(\frac{dy}{dx}\right)^3 \frac{d^2 x}{dy^2} \: =0 Homework Equations Considering that \frac{dy}{dx}=\frac{1}{\frac{dx}{dy}} how does one prove this statement...

Is it possible to find a directional derivative for a point on z = f(x,y) at a point (x,y) in a direction (u1,u2) using the plane tangent to z at (x,y)? If so, how? Thanks!

Homework Statement Prove that (for every x smaller than -1) \displaystyle \frac{1}{2}arctan\frac{2x}{1-x^{2}}+arccotx=\pi Homework Equations The Attempt at a Solution So i split the formula into two parts: \displaystyle \frac{1}{2}arctan\frac{2x}{1-x^{2}} and \displaystyle...

Hi guys, I am trying to create a magnetic field from an image contour and an attempt to create an active contour model. I have a function which takes the image derivative via a Guassian: function J=ImageDerivatives2D(I,sigma,type) % Gaussian based image derivatives % %...

Homework Statement For \mu\geq 0, s\geq 1, prove that (1+s)^{\mu}\geq 1 + s^{\mu} Homework Equations The Attempt at a Solution I have written a proof involving the mean value theorem and derivatives, but there must be a simpler way! I think this should be done purely...

Hi, I remember having read in basic calculus that the following is true, but I don't know what this property is called and am having a hard time finding a reference to this. d u(x,y) = \frac{\partial u}{\partial x} dx + \frac{\partial u}{\partial y} dy Ques: Is this true ? Is this true for...

Here is an example... d/dz(dp/dx) = d/dx(dp/dz) I don't remember learning this in my calculus or differential equations classes unless it was called something else.

I don't post many questions here since I'm usually able to find most of my answers before starting a thread. As only a few of you may know I'm gradually teaching myself calculus. What can I say? I guess I'm that kind of guy. I've managed to pick up on quite a few good basic ideas. There is...

Hi, I've begun learning about General Relativity, though I've already had some exposure to differential geometry. In particular, I understand that Lie Differentiation is a more "primitive" process than Covariant Differentiation (in that the latter requires some sort of connection). My...

I know that for any C2 function, the mixed second-order partials are equal, and I see that this should extend inductively to a statement about the kth partials of a Ck function, but I am having trouble figuring out exactly how this works. For example, take f:ℝ2 → ℝ . fxxy=fxyy is not true...

Hey guys, one quick question about Wick contractions and derivatives: Suppose I want to write down all (non-vacuum) Wick contractions of two fields a, and one field A into a cubic QCD-like interaction term of the form \partial^\nu A^{\mu, a}(p_1) a_\mu^b(p_2) a_\nu^c(p_3) f^{abc} to...

Homework Statement We want to construct a box with a square base and we only have 10 m2 of material to use in construction of the box. Assuming that all the material is used in the construction process determine the maximum volume that the box can have. Homework Equations Chain rule...

Hi there, just wanted to make a clarification before my final exam. The second derivative test for partial derivatives (or at least part of it) states if D = ∂2f/∂x2 * ∂2f/∂y2 - (∂2f/∂x∂y)2 and (a,b) is a critical point of f, then a) if D(a,b) > 0 and ∂2f/∂x2 < 0, then there is a local...

Homework Statement The Hyperbolic coordinate system is given by: u=2xy and v=x^2 - y^2 a.) Find the unit vectors u and v in terms of u,v,x(hat),y(hat) b.)Find the time derivatives of u(hat) and v(hat), your answers will have du/dt and dv/dt in them Homework Equations None really...

Homework Statement Let's say an object is moving with x(t)= e^(-1/t^2) it's motion is continuous everywhere and differentiable because its exponential so v(t)= 2e^(-1/t^2)/t^3 a(t)= e^(-1/t^2) *(4-6t^2)/t^6 I have asked to a calculus teacher and he said all the derivatives will be 0 at...

Homework Statement http://i.imgur.com/DQMRG.jpg Homework Equations The intervals are going by ones. The Attempt at a Solution Well for the first derivative, I'm guessing from -infinity to -1, it's a decreasing line? Also from -1 to 1...it's a constant negative line? I dunno

Could someone please explain the partial and covariant derivatives with upstairs index that appears all of a sudden in Wald in section 4.2 with no explanation? I haven't seen it anywhere else. Homework Statement (n,m)→(n+1,m) derivatives Homework Equations section 4.2--when the...

Homework Statement Find the Taylor series expansion of f(x) = (x-1)/(1+(x-1)^2) about x=1 and use this to compute f(9)(1) and f(10)(1) Homework Equations The sum from n=0 to infinity of f(k)(c)/(k!) (x-c)k The Attempt at a Solution I'm not sure how to approach this...

derivative of integral over e^t to t^5 (sqrt(8+x^4)) dx I know I need to use the chain rule and I can take the derivative of the integral without respect to e^t and t^5. If you know the answer, can you answer and tell me how to do it?! Calculus final on Monday...

The question asks the student to use Taylor's formula to calculate the exact values of higher derivatives f '[0], f '' [0], f ''' [0], ... , f^6'[0] of the function f[x] defined by the power series x/2 + x^2/12 + x^3/240 +x^4/10080 + ... +((k x^k)/(2 k)!) + ... My first...

Homework Statement Find (x,y) which maximizes f(x,y) for x ≥ 0. f(x,y) = e-x - e-2x + (1 - e-x)(4/5 - (3/4 - y)2)Homework Equations The Attempt at a Solution Due to the question prior to this one, I know all the first order and second order partial derivatives of the formula. I do not...

How does higher order derivatives affect the graph? Mostly just the 3rd, 4th or 5th derivatives. I believe I have found the 3rd one but I'm not sure about it or the others.

Hi physics forums, this post may seem like it has lots of questions, but don't think that you are doing ''my homework for me,'' it's actually a huge assignment, in which I am only going to ask a few questions about. this question is actualy easy (or seems to be), but i keep getting 64/3...

Homework Statement When two resistors R1 and R2 are connected in parallel, their effective resistance R = (R1R2)/(R1+R2). Show that is R1 and R2 are both increased by a small percentage c, then the percentage increase of R is also c. Homework Equations The Attempt at a Solution I...

I am exploring the motion of a particle who's path P(x,y) is given by two parametric equations: x = f(t) = a cos(bt) + cd (1) y = g(t) = a sin(bt) (2) To get a tangential velocity for this particle, I differentiated (1) and (2) then combined them using the form sqrt( m2 + n2...

In equation (5.35) the constant drops out when the derivative with respect to r is taken. However, in equation (5.36) the constant does not drop out. Does anybody know why? Equation (5.35) F_L=-\frac {d}{dr}\left(\frac {n^2h^2}{2\mu r^2}\right)=\frac{n^2h^2}{\mu r^3} Equation (5.36)...

Hello All, This problem comes from #18 of section 4.3 out of stewarts 6th edition. The Question: Consider the following function: f(x)= e^(-x) * sqrt(x) What I am trying to find. a.) Find the intervals on which f is increasing and decreasing. b.) find any relative extrema. c.)...

Homework Statement Determine the domain and find the derivative f(x) = ln|(x+2)/(x3 - 1)| Homework Equations The Attempt at a Solution We can factor x3 - 1 = (x-1)(x2) + x + 1) From this we know that x ≠ 1 or -2 because 1 would be undefined at -2 would cause the function to...

Homework Statement a.) f(x)=tan2(x) b.) cos3(x2) c.) (2x-1)/(5x+2) d.) (sqrt(x2-2x))(secx) e.) f(x)=((2x+3)/(x+7))3/2 f.) [sin(x)cos(x)]2 Homework Equations chain rule Product rule Quotient rule Power rule The Attempt at a Solution a.) would you do the power rule...

Homework Statement Find a sequence of differentiable functions $f_n\colon [a,b]\rightarrow\mathbb(R)$ s.t.: --there exists $M>0$ with $|f_n'(x)|\leq M$ for all $n\in\mathbb{N}$ and $x\in[a,b]$; --for all $n\in\mathbb{N}$, $|f_n(a)|\leq M$; --$(g_n)$ is a convergent subsequence with...

Homework Statement Let F(x,y) be a twice differentiable function such that 4 * Fx2 + Fy2 = 0. Set x = u2 - v2 and y = u*v. Show that Fu2 + Fv2 = 0The Attempt at a Solution Fu = Fx*2u + Fy*v Fv = Fx*-2v + Fy*u Fu2 = 4v2Fx2-4FxFy*u*v+Fy2u2 Fv2 = 4u2Fx2+4FxFy*u*v+Fy2v2 Adding these two...

Problem - Find backward finite difference approximations to first, second and third order derivatives to error of order h^3 Attempt By Tailor’s series expansion f(x-h) = f(x) - h f’(x) + h^2/2! f’’(x) - h^3/3! f’’’(x) + … Therefore, f’(x) with error of order h^3 is given by f(x-h) = f(x)...

Homework Statement So there is an exercise in which I should "verify" the chain rule for some functions. In other words to do it by substitution, then doing by the formula and checking if the results are the same. (and checking with the book`s answer too) For a few of them, they just don`t...

Hi, in general can we tell anything about the partial derivatives of a differentiable function if they are equal? for example I would like them to have to equal some constant. Would this be true?

Is this work right?...

Homework Statement A function f(x) has a periodic derivative. In other words f ' (x + p) = f ' (x) for some real value of p. Is f(x) necessarily periodic? Prove or give a counterexample. Homework Equations Periodic functions and Periodic Derivatives The Attempt at a Solution To be...

Homework Statement Consider the system of equations x^2y+za+b^2=1 y^3z+x-ab=0 xb+ya+xyz=-1 1. Can the system be solved for x, y, z as functions of a and b near the point (x, y, z, a, b)=(-1, 1, 1, 0, 0)? 2. Find \frac{\partial x}{\partial a} where x=x(a, b) The Attempt at a...

Homework Statement Let p be an arbitrary polynomial p(x) = anxn + an-1xn-1 + ... + a1x + a0, an cannot equal 0. a) Find (dn/dxn)[p(x)] b)What is (dk/dxk)[p(x)] for k>n Homework Equations The Attempt at a Solution Im actually not really sure what to do for this question...

Homework Statement Let h(t) = tan(3t+7) Find h'(t) and h''(t) I found h'(t) which is equal to 3(sec(3t+7))^2 But I can't seem to find h''(t) How do I find the derivative of this? Could someone please teach me? Is it a composition function? If it is, I think I see 4 functions...

In ordinary multivariable calculus the following situation is common: We have some letters, say, x, y, z and call them variables. We have some relations, say, there is only one f(x,y,z)=0. Then you have to choose your dependent variable and two (three variables minus one relation)...

Homework Statement I need to prove that x\frac{ \partial^2z}{ \partial x^2} + y\frac{\partial^2z}{\partial y\partial x} = 2\frac{\partial z}{\partial x} Homework Equations z = \frac{x^2y^2}{x+y} The Attempt at a Solution I actually did it the long way and I got the right answer...

Homework Statement Let f(x) = sqrt(sin(e^(x^4*sinx))) Find f '(x) I tried this many times and it's really frustrating! I made it a composition function : f(g(h(x))) but I'm not getting the answer at all. At the end, I found : 1/2(sin(e^((x^4)(sinx))))^(-1/2) (cos(e^(x^4...

Homework Statement I made a thread last week where I had a reasonable idea what was going on in 2 problems last week this week I have 2 problems where i have NO idea where to start. Show that the ellipse x2 +2 y2 =2 and the hyperbola 2 x2 - 2 y2 =1 intersect at right angles. What is the...

The question I'm trying to solve is part (ii) of the attached file I've used partial derivatives to input back into the Black Scholes equations and after factorising it, I've got it down to: (a + 2bt + αt +r) * (S².c.e^(at+bt²) = 0 I'm now stuck on what to do next, as there would need to be...

Homework Statement Given F(x_1,x_2,...,x_i,...,x_n) = nth-root(x_1*x_2*...*x_i*...*x_n), how do I take the partial derivative with respect to x_i, where x_i is an arbitrary variable? Homework Equations The Attempt at a Solution Would it just be...

Homework Statement Find a point P on y=x3 such that the tangent at P intersects the original curve again at point Q so that the slope of the tangent at Q is 4 times the slope of the tangent at P. Homework Equations y'=3x2 and the slope of the what I think it should be a secant...

1. The problem statement, all variables and given known data Find the partial derivatives (1st order) of this function: ln((\sqrt{(x^2+y^2} - x)/(\sqrt{x^2+y^2} + x)) Homework Equations The Attempt at a Solution I obviously separated the logarithm quotient into a...