Implicit Definition and 537 Threads

Let me first say i just learned implicit differentiation (earlier today) and i am also new in general to derivatives. I am finding implicit differentiation difficult but i want to understand it before we go over it in class. Homework Statement This is a example in my book. I have been trying...

Homework Statement find y' given x3+y2+x+y=2 Homework Equations The Attempt at a Solution dy/dx=3x2+2y(y')+1+y' I know that's wrong because my 89 gives it as y'=(-3x2+1)/(2y+1), I don't know how to get there though and what happened to the =2. Thanks

Homework Statement 2XY = Y^2 prove that y''2 = \frac{y^{2}-2xy}{(y-x)^3} EDIT: Sorry, don't know how to insert a space in Latex. Homework Equations The Attempt at a Solution 2y+2x \frac{dy}{dx} = 2y \frac{dy}{dx} \frac{dy}{dx}(2y-2x) = 2y \frac{dy}{dx}= \frac{y}{y-x}...

Hi everybody. I have an impicit function that I want to solve numerically in mathematica it looks like: f[x] == b1 \!\( \*SubsuperscriptBox[\(\[Integral]\), \(0\), \(L\)]\(c[ x, \[Alpha]] f[\[Alpha]] SuperscriptBox[\(E\), \(-\( \*SubsuperscriptBox[\(\[Integral]\), \(0\)...

Homework Statement differentiate: yx = y / sqrt(x2 + y2) Homework Equations The Attempt at a Solution I solved this problem by taking the ln of both sides and then solving. It seems from the context of the problem set that this was supposed to be easier than that. Am I...

Sorry for the wordiness of the thread title. Basically I'm wondering, if you have two implicit functions, F(x,y)=0 and G(x,y)=0 (typically rational functions with numerator and denominator very high degree polynomials), both dependent upon the same K (in my case > 34) dimensional set of...

how to identify whether a function is implicit or explicit? advanced thanks.

At first sight this seems like a beautiful paper. Or at least a refreshing one (like opening a window on a good day.) MTd2 spotted it for us. http://arxiv.org/abs/1008.3345 Deformed Special Relativity from Asymptotically Safe Gravity Xavier Calmet, Sabine Hossenfelder, Roberto Percacci...

Implicit differentiation, what's going wrong!? Hey people can someone point out to me please where I'm going wrong with part B of this question, can't get it to look the answer in the book, d2y/dx2 = -3(x^6/y^7)- 3(x^2/y^3). My answer is listed below under part B section, but i can't...

Homework Statement Find d2y/dx2 for cos y + x2 =12 The first derivative I think is correct but the second I am unsure of, this is Q5 of 10 in an assignment and every other question has been far cleaner and easier making me think that I've missed something. We don't have to use implicit...

Homework Statement Find the equation of a tangent line at the curve at point (-3√3, 1) x^(1/3) + y^(1/3) = 4Homework Equations Point-slope: y-1=m(x-1) The Attempt at a Solution I took the derivative of that equation and resulted in -y^(2/3)/x^(2/3) When I tried plugging in x and y to...

Hello, This is my first post here on Physics Forums. Hope to have a good time here. I am currently a phd-student in Denmark within a project covering applied research into applications of computer vision and physics to the seed cleaning industry. This is the only post that will include this...

Good day everybody! In my Numerical Methods textbook (Applied Numerical Analysis, 7ed, Gerald and Wheatley) the authors derive two equations for the ADI method to be used in an iteration scheme. For row-wise traversions, they get...

Homework Statement A conical tent must contain 40\pi ft^{3}. Compute the height and radius of the tent with minimal total surface area. (Include the floor material.) Homework Equations 1. \frac{\pi r^{2} h}{3} = 40\pi 2. \pi r \sqrt{r^{2} + h^{2}} + \pi r^{2} = S 3. \frac {dr}{dh} =...

can someone show me step by step how to find dy/dx of y=1/(x+y) using implicit differentiation?

Social Networks are ways of representing formal links between people. We often make it explicit using befriending mechanisms but their are also implicit methods, like if two people published a similar paper together. On a forum people post information from a variety of sources. The similarity in...

An example of implicit differentation in Stewart, 6th ed, p 883, is given as follows: x^3 + y^3 + z^3 + 6xyz = 1 Differentiating to find dz/dx, 3x^2 + 3z^2(dz/dx) + 6yz + 6xy(dz/dx) = 0 where the product rule was used to differentiate 6xyz with respect to x. Why isn't the...

1. I'm pretty sure I've got this right.. just needing a check. Cheers! 2. x^2+2xy-y^2+x^2=2 3. 2x+2x(dy/dx)+2y-2y(dy/dx)+2x=0 2x(dy/dx)-2y(dy/dx)=-4x-2y dy/dx(2x-2y)=-4x-2y dy/dx=(-4x-2y)/(2x-2y)

Homework Statement I am using Crank–Nicolson to solve a logistic function, modeling population growth. To get the next time step, I have to solve a quadratic equation. The problem is that i get two solutions for y(i+1). Does it mean that I am doing it wrong? If not, can I just pick the...

Homework Statement If T is implicitly defined via the relationship f(x, y, z, T) = 0 to be a differentiable function of x, y and z, show that the first partial derivative of T with respect to z can be found using: \frac{\partial T}{\partial z} = -\frac{\partial f}{\partial z} / \frac{\partial...

Homework Statement If y= \ln \sqrt{xy} , find the value of dy/dx when y=1 Homework Equations The Attempt at a Solution \frac{dy}{dx} = \frac{1}{\sqrt{xy}} \cdot \frac{1}{2\sqrt{xy}}\cdot (x\frac{dy}{dx}+y) \frac{dy}{dx}=\frac{1}{x} , when y=1

Homework Statement Determine dy/dx xy^-2 = 1 Homework Equations The Attempt at a Solution Here's what I tried: y^-2 - 2xy^-3(dy/dx) = 1 dy/dx = (y - y^3)/2x The answer in the book is y/2x. How do you do it?

Homework Statement If siny=2sinx and (dy/dx)^2=1+3sec^2(y) show that: by differentiating 1+3sec^2(y) with respect to x, d^2y/dx^2=3sec^2(y)tan(y) Homework Equations The Attempt at a Solution

find explicit function or functions corresponding from implicit ,,, Homework Statement 1) 4x^2+9y^2=36 2)xy^2 + (x^2-1)y-x=0 The Attempt at a Solution 1) y=√((36-4x^2)/9)==>6/3√(-4x^2)) = 2√(-4x^2)) and the book answer is ±2/3 √(9-x^2) can someone tell me what's my mistake ? 2) well i...

Homework Statement Water flows from a tank of constant cross-sectional area 54 ft2 through an orifice of constant cross-sectional area 1.7 ft2 located at the bottom of the tank. Initially the height of the water in the tank was 20 and its height t sec later is given by the following...

Homework Statement Find y''(x) of the parametric equation 9x^2+y^2=9 using implicit differentiation. Homework Equations I already came up with y'(x) = -9x/y The Attempt at a Solution Here is what I have for y''(x) so far y''(x) = d/dx (-9xy^-1) =-9(d/dx)(xy^-1)...

Hi all, I'm writing myself a ordinary differential equation solver and I've already implemented several explicit integrators, which were pretty easy for me to do. Now I've decided to work on some implicit methods (for any stiff equations) and I've run into some issues. The most basic one is...

Homework Statement Could anyone explain that I got two different answers for this question: find dy/dx of \frac{x}{x+y}-\frac{y}{x}=4 Homework Equations The Attempt at a Solution 1. using quotient rule: \frac{x+y-(1+dy/dx)x}{(x+y)^{2}}-\frac{x\frac{dy}{dx}-y}{x^{2}}=0...

Could anyone explain that I got two different answers for this question: find dy/dx of \frac{x}{x+y}-\frac{y}{x}=4. 1. using quotient rule: \frac{x+y-(1+dy/dx)x}{(x+y)^{2}}-\frac{x\frac{dy}{dx}-y}{x^{2}}=0...

The function of a line is y^2 + x^3 = 9. I calculated the slope of its tangent to be -3x^2/2y. The question asked us to find a point(s) so that the equation of its tangent line is y + 6x = 13. So it's slope must be -6 at that point. I got (2,1) as a point. Are there more than one, or is that...

Homework Statement I have to find an implicit rule for this pattern, Can Someone please help me? 3, 9, 81, 65, 61, 37,... and so on Homework Equations Im stuck not sure how to approach and therefore get a rule The Attempt at a Solution I tried using the arithmetic and geometric formulas...

Homework Statement Use implicit differentiation to find an equation of the tangent line to the cardioid at the point (0, 0.5). x2 + y2 = (2x2 + 2y2 - x)2Homework Equations Derivative rules point slope formula The Attempt at a Solution I got y' = [16x3-4x2+16xy2-4y2-4y2-8x2+2x] / [2y -...

Homework Statement 2x^{2} - 3y^{2} = 4 Homework Equations We say that y is an implicit function of x if we are given an equation: \sigma(x,y) = \tau(x,y) Then to differentiate we do: \frac {d(\sigma(x,y))} {dx} = \frac {d(\tau(x,y))} {dx} The Attempt at a Solution...

Ok so this is a fairly stupid question I'm sure, but I'm not quite clear about the following: Given a Lorentz transformation we require the following to hold: g_{\sigma\rho}\Lambda^{\sigma}_{\mu}\Lambda^{\rho}_{\nu} = g_{\mu\nu} In other notation this is written: \Lambda^{T}g\Lambda...

Homework Statement Find the derivative of the following function. Simplify where possible. y=31*arctan(sqrt(x)) Homework Equations I know that the derivative of arctan(x) = 1 / (1+x2) I also know we will be using chain rule and product rule. The Attempt at a Solution y' =...

I have a function z=f(xz+y) and I want to find the partial differential of z with respect to y (it's a general sort of question, I only need it in terms of the variables already given). My answer would be just partial df/dy but this isn't the right answer. I'm not too hot on partial...

I have a question thus: If (x + y)sin(xy) = 1 find dy/dx. It looks to me as I should use the product rule. d/dx(x + y) I get 1 + dy/dx Now this is where it gets kinda tricky. d/dx sin(xy) its the fuction of a function I think! I get (eventually) cos(xy)xdy/dx + y Now putting...

Homework Statement Use implicit differentiation to find dy/dx if y - sin(xy) = x^2. What I've got is dy/dx y - cos(xy)(y+x dy/dx) = 2x I don't know what I did and I don't know where to go from here.

Homework Statement find \frac{\mathrm{d}y}{\mathrm{d}x} where y is defined implicitly as a function of x Homework Equations x\sin(xy)=x The Attempt at a Solution x(\cos(xy)(x\frac{\mathrm{d}y}{\mathrm{d}x}+y))+\sin(xy)=1...

? i used the implicit function theorem to find dy/dx, then applied that to the arc length formula, but i have to integrate with respect to x and there is the implicit function y[x] inside the radical. also, if it matters, the curve is assumed to be closed.

Prove that if P(a,b) is a point on the rotated ellipse C (whose equation is x^2 -xy +y^2=4 ), then so is Q(-a,-b), and that the tangent lines to C at P and Q are parallel. The equation of the line joining P and Q is y - b = m(x - a), where m= \frac{b-(-b)}{a-(-a)} = \frac{b}{a}, then the...

Homework Statement A swimming pool is 40 feet long, 20 feet wide, 4 feet deep at the shallow end, and 9 feet deep at the deep end. Water is being pumped into the pool at 10 cubic feet per minute. a. When the water is 3 feet deep at the shallow end, at what rate is the water level rising? b...

Homework Statement "An air traffic controller spots two planes at the same altitude converging on a point as they fly at right angles to each other. One plane is 120 miles from the point and is moving at 400 miles per hour. The other plane is 160 miles from the point and has a speed of...

hello, I am an animation student at bournemouth university in England, I am writing a material simulator for my final major project ( some preliminary results http://www.youtube.com/user/jorjpimm ). The final idea is to have elastic, plastic and tearing and breaking material characteristics, all...

Homework Statement Consider the implicit function y(x) defined by the equation cos(x-y)=xy for x>0.5 a.find the smallest two positive values x>0.5 for which y(x)=0 b.find the global minimum of y(x) for x>0.5 c.call the numbers you found inpart(b) x1 and x2 find integral of y(x)dx from x1...

Hi all, I am trying to implement the backward euler integration (in c++) for the pendulum problem. I have the forward euler implemented, but frankly I don't know where to even start from for the implicit integration. I understand the update expressions for implicit, and of course the...

Graphing Implicit Function Homework Statement Graph (x^2+Y^2)^2=4xy A)Find Y' B)Find all points that have vertical tangent lines. C)Find all points that have horizontal tangent lines. The Attempt at a Solution I feel like I'm going nuts on this problem, y' is...

Homework Statement Find all the points on the curve x^{2}y^{2}+xy=2 where the slope of the tangent line is -1. The Attempt at a Solution I differentiated both sides of the equation and got: \frac{dy}{dx}=\frac{-2xy^{2}-y}{x^{2}2y+x} I know that \frac{dy}{dx}=-1, but if I substitute...

Homework Statement Given the equation y= f(x) , at a certain point the slope of the curve is 1/2 and the x-coordinate decreases at 3 units/s. At that point, how fast is the y-coordinate of the object changing? The Attempt at a Solution Dy/dx = f ' (x) dx/dt Would that be...

i have a relation z4 + x2z = x5 , now i differenciate it implictly to find dz/dx , but if we observe carefully we have a relation between x and z , but not a function of x , so is this derivative correct or even if implicit Differenciation valid over here ??