Implicit Definition and 520 Threads

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...

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 ??

Homework Statement Consider: x^3+y^3+2xy=4, y=1 when x=1 a.) Find the equation of the tangent line to the curve when x=1. b.) Find y'' at x=1. c.) Is the graph of y=f(x) concave up or concave down near x=1? Homework Equations Any derivative rules... The Attempt at a Solution For Part a...

Find d^2/dx^2(3y^2+8y=3x) I managed to get dy/dx = 3 / (6y + 8) but I have no clue where to go from here. According to WolfRamAlpha, the answer is -27/(4(16 + 9x)(4 + 3y)), but since dy/dx doesn't have any x value in it, I don't see how the derivative of it would. I've played around...

Homework Statement Find y´(x) for x + y = 1/x^2 + 8/y^2 Homework Equations The Attempt at a Solution Rewrite the eq. as x + y = x^-2 + 8y^-2 differentiate. 1 + y´(x) = (-2x^-3) + (-16y^-3)(y´(x)) Rearrange 1 + (2x^-3) = (-16y^-3)(y´(x)) - (y´(x)) (1 + (2x^-3))/(16y^-3) =...

Homework Statement Find dy/dx of this equation - y*sec(x)=3x*tan(y) Homework Equations -product rule -derivative of sec(x) with respect to x is sec(x)tan(x) i believe -derivative of tan(x) is sec^2(x) i believe The Attempt at a Solution y*sec(x)=3x*tan(y)...

Homework Statement Implicit Differentiation:Use implicit differentiation to find an equation of the tangent line to the curve at the given point. x2/3 + y2/3 = 4 at (-3*31/2,1) Homework Equations ? None? The Attempt at a Solution 2/3 * x-1/3 + 2/3y-1/3*y' = 0 then after a few...

I need to solve this implicit function of the catenary k=cosh(k/sqrt(k^2-1)) how do i Do this in mathematica?

Homework Statement Find dy/dx ; sqrt(xy) = 1 + yx^2 or 0 = 1 + yx^2 - sqrt(xy) Definition : dy/dx = - F_x / F_y; A = F_x = 2xy - 1/2 (xy)^-0.5 * y B = F_y = x^2 - 1/2(xy)^-0.5 * x Then dy/dx = -A / B But the answer according to the book, is this : 4(xy)^-1.5 - y...

Hi. So I'm reading a physics book and I come across the following passage: Ok, up to this point I'm fairly confident I'm following along. But then they do the following: and I have no idea where this comes from. I am guessing here that p_i=\phi _i(q) is only in some sufficiently small...

Homework Statement Find y'' by implicit differentiation. Homework Equations The Attempt at a Solution I get to this point in the problem, which is I solved for y'. But then when I attempt to take y'', in other words take the derivative of my answer for y', I...

2xy=3x-y^2 find dy/dx and d2y/dx2 I just want to make sure my answer is right and simplified I got dy/dx= (3-2y)/ (2x+2y) Now d2y/dx2 took some time but this is what i got: (-12x+2x2y+9+4yx-14y-4y^2) / ((x+y)(2x+2y)^2)

1. use implicit differentiation to evaluate y(prime) for x^3+y^3=4xy+1 at the point (2,1)

so to solve this i differentiated each part and got 6dy/dx + 8 = cos(xy^2)(y^2*x2ydy/dx) then i divided both sides by cos(xy^2) then serpatated the 6dy/dx + 8 and put them both over cos(xy^2) then i took out a yprime and ended up with -8/(6-2y^3xcos(xy^2)) as an answer but its wrong...