Derivatives Definition and 1000 Threads

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)...

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...

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...

Homework Statement If f(x)=\sqrt{x}g(x), where g(4)=8 and g'(4)=7, find f'(4). Homework Equations the product rule/quotient rule The Attempt at a Solution I am having trouble getting this problem started. Would I solve for the x of f(x)?

Homework Statement A) if http://www4d.wolframalpha.com/Calculate/MSP/MSP10819hf7feh5hf5hh7e00004ga728h1d42i6h0c?MSPStoreType=image/gif&s=18&w=161&h=20 Find the partial derivatives? B) Suppose you are manufacturing blackboards and whiteboards and that P is your monthly profit when your...

Find the directional derivative of: f(x,y) = (x^2)y-y^3, (2,1,3) Can somebody explain to me why we did the step we did? First we found the directional derivative of f(x,y,z) ▽f(x,y) = <2xy, (x^2)-3(y^2), a> ▽f(2,1) = <2(2)(1), (2^2)-3(1^2)), a> = <2(2), 4-3, a> = <4,1, a> and then we... did...

Homework Statement h(t) = √t (1 - t^2) Homework Equations the product rule is (first) x (derivative of the second) + (second) x (derivative of the first) The Attempt at a Solution i've been working at this for a while. the closest answer i came up with was this: h(t)= t^1/2 (t^1/2 -...

Homework Statement 2 problems. 1) Find an example of a function f such that : the line y=2 is a horizontal asymptote of the curve y=f(x) the curve intersects the line y=2 at the infinitive number of points 2) The position of an object moving along x-axis is given at time t by: s(t)= 4t-4 if...

The Office of the US Currency Comptroller has an interesting chart 4 titled '5 Banks Dominate in Derivatives, Insured U.S. Commercial Banks, Second Quarter 2011'. http://www.occ.gov/topics/capital-markets/financial-markets/trading/derivatives/dq211.pdf I'm speechless!

Homework Statement A metal bar of length l in the figure below has one end attached at a point P to a circle ofradius a < l. Point Q at the other end can slide back and forth along the x–axis. (a) Find x as a function of θ (θ=angle POQ). (b) Assume the lengths are in centimeters and the...

Homework Statement This is a bonus problem on our homework, and I'm having trouble figuring out how to setup what I need. Homework Equations Here are my best guesses: f_x=\frac{\partial f}{\partial x} f_y=\frac{\partial f}{\partial y} f_{xx}=\frac{\partial}{\partial...

The maximum rate of change of f at the given point and the direction in which it occurs. f(x,y)=(y^2)/x, (2,4) Answer: 4√2, <-1,1> _________________________ For this problem, since I couldn't find the upside down triangle, I am going to use delta to represent the gradient of a function...

find the derivatives of differentiation of trigonometric functions 1. y=cos(3x^2+8x-2) 2. y=tan^3 2x 3. y=sin5x sin^5 x 4. y=Square root of 4sin^2x+9cos^2x help here please.. i can't understand trigonometric functions sorry admin or moderator, i just search the net on how...

1. Hello there, I have a few questions on the derivative homework that I did but not sure if it's right or not. These are difficult and my teacher doesn't go over all of them so I don't know if it is right or not. Please help me so I can understand the concepts before the upcoming test. 1...

Homework Statement can anyone explain me about Integrals and derivatives in brief Homework Equations The Attempt at a Solution

Hi to all of Physics forums community :), I'm not sure whether or not I am in the right section. If not, I apologize for my mistake. Also, I am new to Calculus (I am in Cegep --> Quebec schooling system...) and I am taking Calculus 1 single variable. My teacher just started our class by...

Homework Statement Hello, My first post here I have a numerical problem for Matlab but I get stuck with the basic math... For a circuit I have three equations: 1.Inductance: L=Lo/(1+I^2) 2.Voltage over the inductance: V=L*dI/dt 3.Current over a condensator: I=-C*dV/dt...

In James Stewart's Calculus exercise 82 page 891 asks you to show that: \frac{\partial P}{\partial V}\frac{\partial V}{\partial T}\frac{\partial T}{\partial P} = -1 I can do this by noting that V = \frac{nRT}{P} so that: \frac{\partial V}{\partial T} = \frac{\partial}{\partial...

I have the PDE: (v_r)^2+(v_z)^2=p^2 where v=v(r,z), p=p(r,z). I have some boundary conditions, of sorts: p=c*r*exp(r/a)exp(z/b) for some constants a,b,c, at r=infinity and z=infinity p=0 at f=r, where (f_r)^2=p*r/v-v*v_r (f_z)^2=p*r/v+v*v_r Is it possible that one could obtain an...

Homework Statement Suppose f(x,y) = 2x^5 + 4xy + 2y^3 g1(u,v) = u^2 - v^2 g2(u,v) = uv h(u,v) = f(g1(u,v), g2(u,v)) Use chain rule to calculate: dh/du (1,-1) and dh/dv (1,-1) Homework Equations The Attempt at a Solution i let h (u,v) = 2(u^2 - v^2)^5 + 4(u^2-v^2)(uv) +...

it's just something thechnical let's say i have the function x2+3x+2 when they say f(x+\Deltax) is it (x+\Deltax)2+2(x+\Deltax)+2 or another way?

Homework Statement cot^2(Cos\theta)Homework Equations chain rule f prime (x) = f prime(g(x) * g prime (x) The Attempt at a Solution I am not sure if I am just inputting the wrong numbers into webassign or I am just missing and important trig derivative and just completely off of the boat...

Homework Statement Hi I'm just looking for a link to the proof of this theorem: if the partial derivatives of function f exist and are continuous at a point then the function is differentiable there Or even the name would be helpful Its not a homework assignment per say, just something...

Hello, if I have a fundamental solution, ,f, to a partial differential equation L(f)=0, where L is the differential operator, is that true that the derivatives of the fundamental solution, like D(f), will also be solution to the partial differential equation? Intuitively, is it because things...