Derivatives Definition and 1000 Threads

This is a small part in converting between rectangular to polar coords for laplace equation with a problem of circular geometry: what I have in my notes: \tan\theta=\frac{y}{x}\implies\sec^{2}\theta\frac{\partial\theta}{\partial x}=\frac{-y}{x^{2}} I can't figure out how he went from...

Homework Statement Let f_n be a sequence of holomorphic functions such that f_n converges to zero uniformly in the disc D1 = {z : |z| < 1}. Prove that f '_n converges to zero uniformly in D = {z : |z| < 1/2}.Homework Equations Cauchy inequalities (estimates from the Cauchy integral formula)The...

Homework Statement Use L'Hopital's rule to calculate the following derivatives. Homework Equations 1. lim x-> pie/2 tan3x/tan5x 2. lim x->0 e^x - 1/sin x 3. lim x->1 e^x - e/In x The Attempt at a Solution i have attempted to solve the...

I understand that, having a function f(x), it's derivative function is the rate of change of f. That df/dx means how much f changes, given an infinitesimal change in x, denoted as dx. In second derivatives,how is d2f / dx2explained ? Help me on the intuition please.

please help about this if f(u,v)=f(y/x,z/x)=0 and z=g(x,y) and show thanks alot

Find the first and second derivative--simplify your answer. y=x tanx I solved the first derivative. y'=(x)(sec^2(x)) +(tanx)(1) y'=xsec^2(x) +tanx I don't know about the second derivative though.

Homework Statement x(t) = -0.01t^3 + t^2 - 20t + 4 Homework Equations Min is when t = 12.3 Max is when t = 54.4 The Attempt at a Solution I got -0.03t^2 + 2t - 20 as the derivative. I substituted in t = 12.3 and 54.4 and got 0.02 and 0.19 which don't seem right at all. Because...

Homework Statement Let z = z (x,y) be a function with x = x(s), y = y(t) satisfying the partial differential equation (Ill write ddz/ddt for the partial derivative of z wrt t and dz/dt for the total derivative of z wrt t, as I have no idea how to use Latex.) ddz/ddt +...

Please help me with the geometric interpretation... I am wondering why they can define u(directional derivative) as dr/ds instead of r(s) ? Below are my interpretations, i don't not know whether I'm right... : The r in dr is <dx,dy,dz> and it refers to the change in position of the graph...

Ok my last post was trivial, but it led to this question Assume f is unbounded and analytic in some domain D, and f' is bounded in D does there exist a function for which the above holds and f'',f''',... are all unbounded in D?

Can someone explain to me what are differential and derivatives used for (intergrals ?) in some well known stuff from dynamics or thermodynamics: dA=Fdr or in thermodynamics PdV For example what is that dV ... why not just V. Why do I sometimes write a=d^2r/dt^2 instead of a=r(:)/t(.)...

Homework Statement I just started in calculus ii ,and I remember that most I didn't use specific rules when dealing with derivatives and I sometimes managed to get away with it(especially in physics. now I have been playing with relations and I got unacceptable results so i will post what I...

Homework Statement (1+4x)^5(3+x-x^2)^8 Homework Equations The Attempt at a Solution I get to this point, but I don't know how to break it down. 5(1+4x)^4(4x)(3+x-x^2)^8+8(3+x-x^2)(1-2x)

Help! Solving Derivatives using "Tables" and Equation on Tangent Line 1. I got a worksheet that was given to me on Derivatives to finish for homework but hardly understand it since my teacher assigned it for the same night and she had taught it I was wondering if an explanation on how to do...

According to wiki "The derivative of a function at a chosen input value describes the best linear approximation of the function near that input value. " Is this to say that that derivatives are not 100% accurate? They're linear approximation? Which is confusing to me, with math being such an...

Homework Statement Given the following graph of h(x), identify: 1. The intervals where h(x) is increasing and decreasing. 2. The local maximum and minimum points of h(x) 3. The intervals where h(x) is concave up and concave down 4. The inflection point 5. Sketch the graph of h'(x) and...

Homework Statement Find the derivative of f(x) = x^2+2x+1Homework Equations f(x + h) - f(x) / h lim(h->0) f (x+h) - f(x) / hThe Attempt at a Solution Hi everyone. I keep calculating the derivative for this function incorrectly. I haven't learned the rules of derivatives yet, I am only using...

Homework Statement A 1.8 m tall student is trying to escape from the minimum security prison in Tono. She runs in a straight line towards the prison wall at a speed of 4.0 m/s. The guards shine a spotlight on the prisoner as she begins to run. The spotlight is located on the ground 30 m...

Homework Statement w(r,\theta)= u(rcos \theta ),rsin( \theta)) for some u(x,y) express \frac{ \partial w}{\partial r} and \frac{ \partial w}{ \partial \theta} in terms of \frac{ \partial u}{ \partial x} and \frac{ \partial u}{ \partial y} Homework Equations rewrite the...

Homework Statement Let f be a differentiable function, defined for all real numbers x, with the following properties: 1. f'(x) = ax^2 + bx 2. f'(1) = 6 and f"(1) = 18 3. \int_{1}^{2} f(x)dx = 18 Find f(x). Homework Equations The Attempt at a Solution Using the first two properties, I...

Let g(x) =x^asin(1/x) if x is not 0 g(x)=0 if x=0 Find a particular value for a such that a) g is differentiable on R but such that g' is unbounded on [0,1]. b) g is differentiable on R with g' continuous but not differentiable at zero c) g is differentiable on R but and g' is...

Homework Statement Sorry I tried to use Latex but it didn't work out :/ Make the change of variables r = x + vt and s = x vt in the wave equation partial^2y/partialx^2-(1/v^2)(partial^2y/partialt^2)=0 Homework Equations...

Sorry it's not the best Latex, I hope that you can still help me grasp this. y=2xy1+y(y1)2; y2=C1(x+1/4C1) So, the solution says to implicitly differentiate and gives y1=C1/2y So, how did they get the derivative to be this? This is the first chapter in my DE class and I'm rusty with my...

Homework Statement Derivatives and elasticity: The demand equation for a product is q = \left(\frac{20-p}{2}\right)^{2} for 0 \leq p \leq 20. a) find all values of p for which demand is elastic. Homework Equations Elasticity: \eta = \frac{p}{q} x \frac{dq}{dp} The Attempt at a...

I couldn't decide whether to place this in the Physics or the Math section of the forums, deep down it is really a Math question for Physics problems. So mods please move if you feel it would be more appropriate in the Physics section. So when doing calculations, I always like to make sure my...

Hello; You can have positive integer derivatives, such as this: \frac{d^{2}}{dx^{2}}(x^{2}) = 2 You can have fractional derivatives too; \frac{d^{\frac{1}{2}}}{dx^{\frac{1}{2}}}(x) = \frac{2\sqrt{x}}{\sqrt{\pi}} But what about negative derivatives? \frac{d^{-2}}{dx^{-2}}(x^{2}) Or even...

Domain of f(x,g(x)), and partial derivatives Watching http://www.khanacademy.org/video/exact-equations-intuition-1--proofy?playlist=Differential%20Equations Khan Academy video on exact equations, I got to wondering: if x is a real number, what is the domain of a function defined by f(x,g(x))...

Homework Statement Find an equation of the tangent line to y = sin x at the point x = 0. Graph both functions on the same set of axes on the interval [-pie/4, pie/4]. What does this illustrate? Homework Equations y = mx + b The Attempt at a Solution y = sin x ---> y' = cos x...

This is a very basic question, but I just started wondering about it. First which is the original quantity and which is the derived one. I mean is the displacement by definition is integral from a to b v(t) dt or is it the distance from the starting point to the finishing point or change in...

Hey there. So during break, I'm going to try and refreshen up what I have learned over the summer on Calculus for next semester. I downloaded the M.I.T video lecture series for Calculus I with David Jerison. The lecture series is good, however I have a question. In his first lecture, he starts...

1. Find the derivatie of y, dy when e/\(y) cos x=1 + sin (xy) --- dx 2. I don't know of any Relevant equations 3. The first time i tried the problem i got e/\(y) cos X+ y cos (xy)...

Homework Statement Heat is being conducted radially through a cylindrical pipe. The temperature at a radius r is T(r). In Cartesian co-ordinates, r = \sqrt{(x^{2}+ y^{2}}) show that \frac{\partial T}{\partial x} = \frac{x}{r} \frac{dT}{dr}

Just a quick question... To calculate a directional derivative of f(x,y) at the point \vec{u} in the direction \hat{v}, can I just use the formula... \nabla f(\vec{u}) . \hat{v}? It would be so easy.

What are the laplace transformations of y"' and y"". Any table I can find only goes up to y". Thanks.

V_{a;b} = V_{a,b} - \Gamma^d_{ad}V_d Now take the second derivative... V_{a;b;c} = (V_{a;b})_{,c} - \Gamma^f_{ac}V_{f;b} - \Gamma^f_{bc}V_{a;f} But I have no idea how to get the parts with the Christoffel symbols. V_{a;b;c} = (V_{a;b})_{,c} - \Gamma^f_{(a;b)c}V_{af} = (V_{a;b})_{,c} -...

Homework Statement I've been given equations that have derivatives as initial conditions, rather than things like u(0,t)=u(L,t)=0 Things like this: http://img444.imageshack.us/img444/5082/mathu.th.jpg Uploaded with ImageShack.us Homework Equations The Attempt at a...

Hi! Please can anyone help me to understand what exactly Integration & derivatives are. Please don't tell in form of limits & continuity. But tell in details of , what we exactly do when we use these functions. Please explain with a practicle example. I will appreciate your efforts...

Homework Statement Using Maple, I'm asked to create a quintic function, in the form of ax^5+bx^4+cx^3+dx^2+ex+f given the following data: It will pass through the points (-5,15), (-5/2, 100), and (10, -5) -f'(5)=(-1) -f''(5)=1 Homework Equations How would I go about doing this? I'm allowed to...

Hi, I'm a new member to the forum, and I'm currently studying Calculus. Basically, derivatives can be written as (dy/dx) in Leibniz's notation, but I remember my teacher saying that it's just a symbol and shouldn't be used like two variables (dy and dx)... However, when there's some integral...

In statistical mechanics we express partial derivatives of functions, keeping some variables fixed. But these variables are functions of the other variables (which are not fixed). I'm just confused by this, what is the convention for taking these derivatives? For example, if we have S as a...

I try to understand how to calculate derivatives of functions, which contain matrices. For a start I am looking at derivatives by a single variable. I have x=f(t) and I want to calculate \frac{dx}{dt}. The caveat is that f contains matrices, that depend on t. Can I use the ordinary chain rule...

In short, I need to know how do you do them. I missed class, and our textbook is so bad that it might as well be written in a foreign language. I understand how to do dy/dx of an equation not in the form y =... ex. y^2 = x^3 + 2x + 5, (y'=(3x^2 +2)/2y) for example, but how would you take the...

How does one take the partial derivatives of a function that is defined implicitly? For example, the function, x^2 / 4 + y^2 + z^2 = 3.

Homework Statement What are the upper derivative and lower derivative of the characteristic function of rationals? Homework Equations The Attempt at a Solution I think they are : upper derivative = 0 lower derivative = negative infinity

Homework Statement What is the relationship with a function's rising, falling, high point or low point to it's derivative? The Attempt at a Solution I have plotted my graphs, I can see that they intersect at the high and low points. But what is the relationship Also on another...

I need to use partial derivatives to prove that u(x,t)=f(x+at)+g(x-at) is a solution to: u_{tt}=a^{2}u_{xx} I'm stuck on how I'm supposed to approach the problem. I'm lost as to what order I should do the derivations in. I tried making a tree diagram, and I came out like this. The arrow...

Now I understand the basic concept that if one derivative's velocity you get acceleration and if you integrate velocity you will get the distance. But what about in this case?Homework Statement Homework Equations The Attempt at a Solution

Homework Statement Using logarithmic differentiation calculate the derivative of y=e^(x^x) The Attempt at a Solution y=e^x^x LNy=LNe^x^x LNy=x^xLNe ... Stuck! This seems to be the only way you can do it, but once I get to that part I'm not sure what else there is to do. I...

I need to find the derivative of the square root of (2x+1) (not sure how to do square root symbol here, sorry) I understand that the square root of (2x+1)= (2x+1)^(1/2), but I am getting a little confused on how to continue from there.

sorry folks i don't even have an idea to this question`s solution so i hope u people may like to help me. i`m stuck to it since last week nd i hope its from partial derivative... please suggest me a book or a hint or the solution. Let a long circular cylinder of unit radius be placed in a large...