What is Implicit: Definition and 535 Discussions

In mathematics, an implicit equation is a relation of the form R(x1,…, xn) = 0, where R is a function of several variables (often a polynomial). For example, the implicit equation of the unit circle is x2 + y2 − 1 = 0.
An implicit function is a function that is defined by an implicit equation, that relates one of the variables, considered as the value of the function, with the others considered as the arguments. For example, the equation x2 + y2 − 1 = 0 of the unit circle defines y as an implicit function of x if –1 ≤ x ≤ 1, and one restricts y to nonnegative values.
The implicit function theorem provides conditions under which some kinds of relations define an implicit function, namely relations defined as the indicator function of the zero set of some continuously differentiable multivariate function.

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  1. S

    Superior implicit differentiation, prove answer.

    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}...
  2. W

    Mathematica Difficult implicit function in mathematica.

    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]\), \(0\)...
  3. J

    Implicit Differentiation Shortcut

    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...
  4. D

    Find Parameter Set for N Intersections of 2 Implicit Functions

    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...
  5. A

    How to identify whether a function is implicit or explicit?

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

    Percacci Calmet Hossenfelder find min length implicit in AsymSafe gravity

    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...
  7. L

    Implicit differentiation, whats going wrong?

    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...
  8. P

    Implicit differentiation - Help

    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...
  9. B

    Implicit Differentiation; Tangent Line

    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...
  10. I

    Implicit function for arbitrary cylinder

    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...
  11. P

    The Alternating Direction Implicit Method in 2-D

    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...
  12. S

    Implicit differentiation and optimization

    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} =...
  13. C

    Finding dy/dx of y=1/(x+y) using implicit differentiation: Step-by-step guide

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

    Implicit Web Based Social Networks on Web Forums

    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...
  15. D

    Implicit differentiation and the product rule

    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...
  16. L

    Implicit Differentiation: Solving for dy/dx

    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)
  17. M

    Implicit numerical differentiation

    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...
  18. R

    Multivariable chain rule (with implicit variable)

    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...
  19. T

    What is the Value of dy/dx When y=1 in Implicit Differentiation?

    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
  20. F

    Implicit differentiation dy/dx

    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?
  21. K

    How Do You Solve for d²y/dx² in Implicit Differentiation?

    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
  22. M

    Find explicit function or functions corresponding from implicit

    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...
  23. P

    How to find the rate of decrease of water height in a tank

    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...
  24. B

    Second Derivative using Implicit Differentiation

    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)...
  25. S

    Solving differential equations using implicit methods

    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...
  26. B

    Implicit Differentiation: two different answers found. Please explain.

    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...
  27. B

    Implicit differentiation: two answers resulted

    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...
  28. B

    Finding Points of Tangency for a Given Tangent Line Equation

    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...
  29. M

    Help with Implicit Formula HW: 3, 9, 81, 65...

    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...
  30. W

    Find Tangent Line to Cardioid at (0, 0.5) Using Implicit Diff.

    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 -...
  31. A

    Implicit Differentiation Clarification

    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...
  32. A

    Explicit and Implicit Matrix Notation Question

    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...
  33. W

    Implicit Derivative of y=31*arctan(x)

    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' =...
  34. A

    Implicit partial differentiation

    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...
  35. J

    What is the Implicit Differentiation of (x + y)sin(xy) = 1?

    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...
  36. S

    How do I use implicit differentiation to find dy/dx in this given equation?

    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.
  37. L

    Implicit differentiation

    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...
  38. O

    How do i find the arc length of an implicit curve given by f[x,y]=0?

    ? 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.
  39. J

    Proof using implicit differentiation

    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...
  40. Salazar

    Swimming Pools and Related Rates along with Implicit Differentiation

    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...
  41. Salazar

    Air Traffic Controller and Related Rates along with Implicit Differentiation

    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...
  42. J

    Implicit integration in large simulation

    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...
  43. T

    Consider the implicit function y(x) defined by the equation

    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...
  44. J

    Backward Euler / Implicit Integration Implementation

    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...
  45. L

    Graphing Implicit Function: Find HTL & VTL

    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...
  46. T

    Finding Points on a Curve with Tangent Line Slope -1

    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...
  47. L

    Implicit Differentiation w/ Composite Function

    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...
  48. P

    Is Implicit Differentiation Valid in Cases Where z is Not a Function of x?

    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 ??
  49. J

    Implicit Differentiation: Finding Tangent Line and Second Derivative

    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...
  50. D

    Understanding Implicit Differentiation: Solving for Second Order Derivatives

    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...
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