Differentiation Definition and 1000 Threads

Hi all, I have to differentiate Ln(x+\frac{1}{x}) where I first differentiate Ln and than multiply by the differentiation of the inner function 1/(x+\frac{1}{x})*(1-\frac{1}{x^2} which I simplify to \frac{x}{x^2+1}*(1-\frac{1}{x^2}) \frac{x}{x^2+1}-\frac{1}{x*(x^2+1)}...

Homework Statement f(x)= x^2(x-2)^4 solve for f '(x) Homework Equations f(x) = x^2(x-2)^4 The Attempt at a Solution 4x^2(x-2)^3 The answer is given in the book as 2x(x-2)^3(3x-2) i'm not following any progression that gets me to that solution regardless of how many times I...

Homework Statement f a differentiable real valued function lim h - > 0 of (f(x + ah) - f(x + bh))/h where a,b real numbers Homework Equations definition of derivative lim h-> 0 of (f(x+h) - f(x))/h The Attempt at a Solution I've picked several functions like x^2 and 1/2x...

Homework Statement I need in proving that the derivative (d^{n}/dx^{n})(sin4x + cos4x) = 4n-1 cos(4x + n\pi/2) The Attempt at a Solution I understand implicit differentiation in basic problems but I get stump with the n exponent in the differentiation symbol; am I suppose to treat it as...

Homework Statement I am given a table of data derived from experiment. A force (F) is applied to a spring and the extension (x) is measured and recorded. An additional column of data for the derivative (dF/dx) is also provided. Here is the data: x(m) F(kN) df/dx (kN/m) 0.0...

Homework Statement Find the coordinates of the point in the first quadrant at which the tangent line to the curve x3-xy+y3=0 is parallel to the x-axis. SO: x= + y= + mtan=0 Homework Equations \frac{dy}{dx}=m_{tan} The Attempt at a Solution \frac{dy}{dx}=\frac{y-3x^{2}}{3y^{2}-x}=0 After I...

I encountered a proof problem when I was reading up on the derivatives of natural logarithms' section. It gave a rule which said this : \text{For } a >0 \text{ and } a\ne 1 \text{,}\\\frac{d}{dx}(a^{u}) \ = \ a^{u} \ \ln{a\frac{du}{dx}} To prove it on my own, I made a few identities: a^{u}=y...

Suppose we are given that d --F(y) = f(y) dy Then is it true that dF(h(u)) -------- = f(h(u)) dh(u)/du ? du Why or why not? In particular, I don't understand how to get the red part... Thanks for explaining!

What is the actual meaning of the notation of df[g(x)] ------- dx Here do we actually differentiate f with respect to x first and then evaluate it at g(x), or do we first evaluate f at g(x), then differentiate it with respect to x? Does the order matter? df --[g(x)] dx d...

1) A particle is moving along the curve y=3sqrt{3x+3}. As the particle passes through the point (2, 9), its x-coordinate increases at a rate of 2 units per second. Find the rate of change of the distance from the particle to the origin at this instant. 2) Use implicit differentiation to find...

Homework Statement Hello guys. I had to do some test corrections for my AP Calculus AB class. I have completed all of them besides the four below. Can anyone tell me where I go wrong? 1. Differentiate y = (1+cosx)/(1-cosx) dy/dx = [(1-cosx)(sinx)-(1+cosx)(sinx)]/(1-cosx)^2...

Homework Statement Use implicit differentiation to find the slope of the tangent line to the curve 4x^2-3xy+1y^3=26 at the point (3,2) The Attempt at a Solution I attempted the problem and i came up with dy/dx= (-8x+4)/(3y^2) which is wrong. Need some help with this.

Homework Statement Determine dy/dx when y*sin(x2)=5 The Attempt at a Solution y*2xcos(x2) dx/dx + sin(x2)*1 dy/dx = 0 2xy cos(x2)*dy/dx = -sin(x2) dy/dx = -sin(x2) / 2xy cos(x2) dy/dx = -2xy tan(x2)

Homework Statement Find the value of dy/dx at x=2 when x2+xy=5 The Attempt at a Solution To find y: 22+2y=5 y=1/2 To find dy/dx: 2x(dx/dx)+x(dy/dx)+y(dx/dx)=0 2x+x(dy/dx)+y=0 (dy/dx)=(-2x-y) / x Plug in y and x: dy/dx=-2(2)-(1/2) / 2 dy/dx=-9/4 when x=2

Homework Statement Find dy/dx for: a) xsin(xy^2) - ln(x/y) = y b) x = 3cos(a), y = 2sec(a). simplify then find dy/dx when a = pi/3 Homework Equations The Attempt at a Solution I've done both of them, was just hoping someone could check I've done things correctly. I'm...

Homework Statement Find the partial of z with respect to x keeping r constant. Homework Equations z=x2+y2 x= rcos(t) y= rsin(t) The Attempt at a Solution= r^2(cos(t))^2 + r^2(sin(t))^2 use product rule on "x" and hold r and y constant = [0(cos(t))^2 + r^2(2cos(t))(-sin(t)))] + 0...

Homework Equations Take the second derivative of: cos(x^2) The Attempt at a Solution cos(x^2) dy/du = -sin(u) du/dx = 2x dy/dx= -2xsin(x^2) I don't know how to begin taking the derivative of this a second time...

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...