Differentiation Definition and 1000 Threads

Homework Statement Let p > 1, and put q = p/(p-1), so 1/p + 1/q = 1. Show that for any x > 0, y > 0, we have xy <= xp/p + yq/q, and find the case where equality holds. Homework Equations The Attempt at a Solution This is in the differentiation chapter of my analysis book (Browder)...

Hi ! Im having a problem with a question! I need to differentiate the equation 1/ root of (3x^2 + 2) ! Using the formula (f(x+delta) - f(x)) / delta ! Your help would be appreciated!

Homework Statement just a check, in Implicit Differentiation if you have let's say (x2+y2)2 would you get 2(x2+y2)(2x+2y(dy/dx)) or would it go out of the whole function in the chain rule and be 2(x2+y2)(2x+2y)(dy/dx) much appreciated.

Homework Statement Implicit Differentiation: I Was given the equation find dy/dx: (3x3y2 + 7x) (x2y3 + 3xy)- The Attempt at a Solution Ok, i know i have to use the product rule on top, and on bottom and the quotient rule for the fraction so... if i set s = 3x3 t = y2 u = (3x3y2 +...

g = GM/r^2.. since g is an acceleration, Can g be written like this?...g = dv/dt differentiation of velocity..Or partial derivative ∂v/∂t...is this correct...wat is the difference between differentiation and partial differentiation..can somebody explain me which is correct...

Another problem I'm not sure of :( find \frac{dy}{dx} for the function xy^{2} + x lnx = 4y my answer y^{2} + x2y \frac{dy}{dx} + lnx + x (1/x) \frac{dy}{dx} = 4\frac{dy}{dx} x2y \frac{dy}{dx} + \frac{dy}{dx} - 4\frac{dy}{dx} = -y ^{2} - lnx \frac{dy}{dx} ( x2y - 3) =...

Dear all I am searching the materials that is related with practical problems. Particularly differentiation and integration equations How does one get into solve to use this equations... Also what are the applications,results how much accuracy with practical ...etc Practical books or...

Use implicit differentiation to find \frac{dy}{dx} for xy^{2} – yx^{2} = 3xy i've answered the question but i think I'm doing it wrong any help is appreciated! x(2y)\frac{dy}{dx} – y(2x) = 3xy 2xy \frac{dy}{dx} – 2yx = 3xy 2xy\frac{dy}{dx} = 5xy \frac{dy}{dx} = \frac{5xy}{2xy}...

Im trying to solve this function, that is part of a larger equation: \frac{d}{dx} xe^y do I need to get rid of the x term so the y term is dy/dx?

Hi everyone, I know that integration is the inverse process of differentiation, and that the definite integral is defined as: \int_{a}^{b} f(x) dx = \lim_{n \to \infty} \sum^{n}_{i = 1} f(x_i) \Delta x assuming that the integrand is defined over the interval [a,b]. My question is: Why is...

Heres another problem I was working on... http://img141.imageshack.us/img141/2318/calc2qg4.jpg Im trying to find dy/dx using implicit differentiation...my algebra is a bit rusty...but I am trying to make sure I am on the right track...

Do you guys know if it's possible to solve for the following integral l(t)=∫ {a+ [b+cL(t)+exp^L(t)]/d } dt where a, b, c and d are constants and the derivative of L(t) is l(t). Thanks in advance!

how do you differentiate these equations: f(x) = x^2 x < 3 x + 6 x >= 3 2. f(x) = abs(3x^2 - 6) 3. f(x) = abs(abs(x) - 1) Thank your for your help.

I know I should know this... it looks so ridiculously easy. In the course of getting d'Alembert's wave equation solution, we get the following equation: 2cp'\left(x\right)=cf'\left(x\right)+g\left(x\right) The primes are derivatives wrt t. Then we re-order the equation and "integrate the...

Homework Statement Use implicit diff to find partial x and partial y if x² + y² + z² = 3xyz The Attempt at a Solution firstly with partial x... 2x + 2z(∂z/∂x) = 3yz + 3xy(∂z/dx) 2x - 3yz = 3xy(∂z/dx) - 2z(∂z/∂x) 2x - 3yz = (3xy - 2z)(∂z/dx) (2x - 3yz)/(3xy - 2z) = (∂z/dx)...

Differentiation Help! Homework Statement A particle is moving along a straight line so that, at time t seconds after leaving a fixed point O, its velocity vms-1 is given by v=10sin(1/2 t). Find the time when the acceleration, given by dv/dt, is first zero. Homework Equations sinx...

Hello! I need some help here please for ppl who are familiar with implicit differentiation. Use implicit differentiation to find dy/dx, in each case say where it is defined; a) y^5 +x^2 y^3 = 1+xy b) y= \frac{x^{3/2}\sqrt{7x^2 +1}}{sin(x) e^{3x^2 + 2x}}, x \neq n\pi n \in Z...

1. The problem statement The formula that must be proven is: d (A∙B) = A∙dB + dA∙B du du du 2. The attempt at a solution When I substitute the left side of the equation to the general formula of vector differentiation...

If I have a function f from RxR to R, and a function g from RxR to RxR. What are the partial derivatives of the composition f(g)? I end up multiplying the derivative of f with g, but g is a vector? The partial derivative should have its image in R.

If I differentiate two unit vectors, one with respect to the other, would it just be the dot product between the two vectors (namely the cosine of the angle between them)? I don't understand the physical meaning of the result...

Hey all- I typed up this little cheat sheet to help me with my learning of derivatives so I though someone else might want to use it for reference. I plan to add to it some examples as well as log and e rules. I will keep you updated if there is any interest in those as well. Enjoy!

Homework Statement \frac{\mathrm{d}\left(\frac{1}{a}\tan ^{-1} \left(\frac{x}{a}\right)\right)}{\mathrm{d}x}2. The attempt at a solution Let y = \frac{1}{a}\tan ^{-1} \left(\frac{x}{a}\right) \therefore x = a \tan \left(ay\right) Differentiate with respect to x \rightarrow 1 = a \sec ^2...

Wolfram has a nice online anti-derivative finder here http://integrals.wolfram.com/index.jsp but I didn't find a corresponding one for differentiation. Does anyone know of an online differentiator?

Homework Statement y^2 = 3x^3 + 2x and y must be positive. Find the normal component of acceleration when: x=3m \dot x = 5ms^{ - 1} \ddot x = 5ms^{ - 2} 2. The attempt at a solution Well my approach would be to differentiate it implicitly twice and solve for {\ddot y}. Then I have...

Does anyone know how to differentiate an exponential, which has an operator in its power? I found it quite a trouble in Peskin's QFT (page 84, formulas (4.17), (4.18)). Here we have these two formulas of Peskin: U\left( t,t_{0}\right)=e^{iH_{0}\left( t-t_{0}\right) }e^{-iH\left(...

so I have a implicit diffentiation problem and was wondering if someone could help me out.. I need to figure out how to get dy/dx=0 so eg if i had dy/dx = 4xy+2x/5y^2 and you want to write this in terms of y, how is this done? is there a trick?

Could someone please explain to me how implicit differentiation is an application of the chain rule? It would be much appreciated. By the way, if it helps, I'm a junior in high school. Thanks.

Homework Statement Find the general solution of y' + (2/x)y = 3/(x^2) The Attempt at a Solution xy' + 2y = 3/x d/dx (x * 2y) = 3/x integrating both sides (using product rule for LHS) I end up with y= (3lnx + C)/2x Then I am supposed to find the solution for which y(2)...

Homework Statement Can we say that Differentiation and Integration (in Calculus) are inverse operation to each other? Thx Homework Equations The Attempt at a Solution

Homework Statement dy/dx: square root x+y= 1+x^3y^2 Homework Equations chain rule implicit differentiation The Attempt at a Solution 1/2 x+y -1/2 =2x^2y^3 *y'

I'm having some trouble with the following question, it was on a test previously and I haven't been able to figure it out :/ Let V=4*L^3 cm^3, where dl/dt=10*t cm/s. Find dV/dt at t=0.1 second

Hi, I'm working on a cal III problem involving implicit differentiation. I have to find the second order partial derivative of an implicit function, basically: \partial2f \partialx2 now, I know that for a single order \partialf/\partialx, I would simply use the chain rule property: \partialf =...

Homework Statement Find dy/dx by implicit differentiation: 6x^2+8xy+y^2=6 Homework Equations n/a The Attempt at a Solution I'm using y'=(dy/dx) I found the derivative of the above problem. 12x+8xy'+10y=0 (I used the product rule to find the derivative of 8xy') 12x+8xy'+10y=0...

Question: Find derivative of f(x)=((x^2)(x^3))/((x^4)(x^2)) Attempt: ln f(x)=(lnx^2)+(lnx^3)-(lnx^4)-(lnx^2) Can someone tell me what I have done wrong so far? Thanks

Im having trouble solving these two questions. I don't know where to start so I can't give an attempt at either of them. Please tell me how to do the full question if you can cause i can't check back until morning then i have to go to an exam. http://www.users.on.net/~rohanlal/one.jpg...

(x^2-y^2)^2=(x+y)^3 I tried to use the chain rule on both sides but it didn't work because y needs to have the chain rule used on it explicitly and if i differentiate y explicitly then use the chain rule on everything i would be finding the 2nd derivative. So how do i differentiate this?

Homework Statement A curve has parametric equaions: x = 2cot t, y = 2sin²t, 0 < t <= pi/2 Find an expression for dy/dx in terms of the parameter t The Attempt at a Solution Not sure where to go. Do i need to make a Cartesian equation first? Thanks :)

[SOLVED] Differentiation of displacement and time to get velocity A moving body is related to a fixed point by the displacement equation: s = 12( 1 - e^-t). Assuming the body is moving in a straight line on a flat plain. 1. obtain an expression for the velocity after time t seconds. 2...

Hey there, this should be a very simple problem, but again, I haven't had much guidance in finding formulas with differentiation. If anyone could help me with this i'd greatly appreciate it as it can help me to understand the others. Characteristics of SHM are displacement (x) and time (t)...

Homework Statement x = 5sin(2y +6) find dy in terms of x Homework Equations The Attempt at a Solution dx/dy = 8 cos (2y+6) dy/dx = 1 / (8cos(2y+6) but according to the mark scheme the final answer is + or - 1 / (2 sqrt[16/x^2]) i don't see how on Earth they got...

Homework Statement Find \frac{dU_{ave}}{d\beta} where U_{ave}=\sum_{k}\left(\frac{U_{k}exp(-U_{k}\beta)}{exp(-U_{k}\beta)}\right) Homework Equations The Attempt at a Solution My answer is supposed to be -(U_{ave}^{2})+(U_{ave})^{2} However I keep getting zero. I can...

Homework Statement (x - h)^2 + (y - k)^2 = r^2 where h,k and r are constants The Attempt at a Solution \begin{array}{l} \frac{d}{{dx}}\left[ {(x - h)^2 + (y - k)^2 } \right] = \frac{d}{{dx}}r^2 \\ 2(x - h) + 2\frac{{dy}}{{dx}}(y - k) = 0 \\ \Rightarrow \frac{{dy}}{{dx}}...

Homework Statement Differentiate f = arctan(u/v) with respect to u The Attempt at a Solution Using the chain rule fu = (1/(1 + (u/v)2)) * 1/v = 1/(v + u2/v) The solutions manual says v/(u2 + v2) What is my mistake?

Homework Statement Prove that if f''(x) exists and is continuous in some neighborhood of a, than we can write f''(a)= \lim_{\substack{h\rightarrow 0}}\frac{f(a+h)- 2f(a)+f(a-h)}{h^2} The Attempt at a Solution I just proved in the first part of the question, not posted, that...

Solved: Real Analysis, differentiation Homework Statement If g is differentiable and g(x+y)=g(x)(g(y) find g(0) and show g'(x)=g'(0)g(x) The Attempt at a Solution I solved g(0)=1 and I got as far as g'(x)=\lim_{\substack{x\rightarrow 0}}g(x) \frac{g(h)-1}{h} but now I...

Homework Statement If dy/dx=xy^2 and x=1 when y=1, then y= (A) x^2 (B) -2/(x^2 -3) (C) x^2 + 3 (D) 2/(x^2 +1) (E) (x^2 -3)/2 Homework Equations The Attempt at a Solution dy/dx=xy^2 dy=xy^2dx dy/y^2=x dx ∫dy/y^2=∫x dx -1/y = x^2/2 + C y=-2/x^2 + C 1=-2/1^2 + C C=3...

helicopter moves vertically. Height above start point = y height at t seconds = y= (1/4)t^4 -26t^2 + 96t t = between 0 and 4 differentiate to find velocity = t^3 + 52t + 96 acceleration = 3t^2-52 thats part 1 of question done, easy.Verify that y has a stationary value when t =...

Homework Statement if g(t)=(10^t)(log...t) then evaluate g'(10) ......10 <---------(my attempt at a log base 10) Homework Equations im completely lost...i don't know if i should take the ln of both sides...or what to do really. The Attempt at a Solution

I need help differentiating this equation: y=(x-1)^2(6^x) What I have (I went wrong somewhere): dy/dx = (x-1)[(x-1)(6^x)] =(x-1)[6^x(1+ x ln6 - ln6) =(x-1)6^x(1+ x ln6 - ln6) So; My final answer: (x-1)6^x(1+ x ln6 - ln6) Answer in the textbook...

Differentiation ---Help, please! 1. Homework Statement 1) Use Newtons Method to approximate the real zero of the function f(x)=x^3 + 7x + 3 = 0 2) The curve y = x^3-2x^2+x-3 intersects the curve y = cos(2x). If x = 1.8 is used as the first estimate then, using Newton's Method, what is the...