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

    Chain rule for several variables: Implicit diff.

    Homework Statement Z is defined implicitly as a function of x,y by equation (z^2)x + 3xy^2 + e^((y^2)z) = 4. Find dz/dx Homework Equations dz/dx = -Fx/FzThe Attempt at a Solution Fx= z^2 + 3y^2 Fz=2zx+(y^2)e^((y^2)z) dz/dx= (z^2+3y^2)/[2zx+(y^2)e^((y^2)z)] I'm not sure if I used the partial...
  2. M

    Implicit differentiation - messed up somewhere

    Homework Statement find d^2y/dx^2 at (1,1) for: x^2y + x^2 -y^2 = 1 Homework Equations none The Attempt at a Solution i worked it all out but the answer I am getting is not an option. could someone show me where i made a mistake? I am not asking you to do the problem for me...
  3. T

    Implicit Function Theorem

    Homework Statement I'm looking for someone to walk me through a problem, because I keep falling further and further behind ... Let f be a real-valued function on he strip R_2: a \leq x \leq b, -\infty < y < \infty . Can the equation f(x,y) = 0 be solved for y as a function of x; f is...
  4. T

    Wierd implicit derivative

    when i took the derivative of X^2*Y^2-2x=6 i didn't get the same thing that i got when i took the derivative of y^2=(6+2x)/x^2 and all i did was rewrite the origional equation. why did rewriting the equation change my answer?
  5. A

    Help with 1 quick implicit differentiation problem

    Homework Statement what is the implicit differentiation ? Homework Equations 2sin(x)cos(y)=1 The Attempt at a Solution d/dx[2sin(x)cos(y)]= d/dx[1] 2cos(x)*-sin(y)*dy/dx=0 I haev a bad feeling i did this wrong...
  6. U

    Implicit differentiation homework

    hi i couldn't solve this question i think there is a mistake in it anyone can check it please ? http://img296.imageshack.us/img296/3716/13055173zr3.png
  7. madmike159

    Solve Implicit Functions: dy/dx of y^2+2y=x^3+3x-1

    Homework Statement Find dy/dx of y^2+2y = x^3+3x-1 Homework Equations The Attempt at a Solution I devided both sides by y so i got y+2 = x^3+3x-1/y then differentiating i got dy/dx = 3x^2 +3 / dy/dx I don't think this is right thanks for any help
  8. K

    Implicit Differentiation and coordinates

    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...
  9. N

    2 Problems. 1 regarding implicit differentiation

    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...
  10. N

    How do I find the slope of a tangent line using implicit differentiation?

    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.
  11. D

    Implicit Differentiation w/ trig functions check

    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)
  12. D

    Check request: Implicit Differentiation

    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
  13. G

    Implicit Differentiation Check

    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.
  14. G

    Implicit Differentiation: Finding dy/dx for a Given Equation

    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 +...
  15. L

    Use implicit differentiation to find dy/dx [Answer check]

    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}...
  16. J

    Implicit differentiation solving a function

    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?
  17. J

    Solving a Calculus Problem with Implicit Differentiation

    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...
  18. T

    Query regarding implicit differentiation

    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)...
  19. R

    When is the derivative of a function defined using implicit differentiation?

    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...
  20. A

    Implicit Function Homework: Finding Min/Max

    Homework Statement Hey. I have this problem with the second part of the question. In the first part, I needed to find all the extrema points of this implicit function and the second one is to find if it's minimum or maximum. I posted only the derivative of the implicit function and the...
  21. S

    Easy Implicit Differentiation Question

    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...
  22. D

    How can I solve this implicit differentiation problem?

    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?
  23. J

    What is Implicit Differentiation and How is it Related to the Chain Rule?

    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.
  24. C

    Implicit 'higher' differentiation

    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 =...
  25. S

    Find dy/dx by implicit differentiation: 6x^2+8xy+y^2=6

    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...
  26. R

    How do I use implicit differentiation to solve these two questions?

    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...
  27. quasar987

    About the implicit function theorem

    In the implicit function theorem, we take a C^1 function F:R^n x R^m --> R^m and given a condition on the partial derivatives at a point (x_0,y_0) such that F(x_0,y_0)=0, we conclude that the relation F(x,y)=0 implicitely defines a function f(x)=y in a nbh of x_0. I.e. the last m variables are...
  28. R

    Implicit Differentiation: Solving for dy/dx in (x^2-y^2)^2=(x+y)^3

    (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?
  29. P

    Independent / Dependent variables for implicit functions

    This probably has a really simple answer. Forr u=x^2-y^2 and v=x^2+y^2 x and y are apparently the dependent variables. But the independent variable is the input while the dependent variable is the output, so since u=f1(x,y) and v=f2(x,y) shouldn't they (u and v) be the dependent variables?
  30. F

    Implicit differentiation to find the slope

    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}}...
  31. A

    Solving Implicit Functions: F1(x), F2(x) near 0

    Hello: I thought I had this but in doing the problem I realized I didn't (or maybe I didn't). One of the problems was that in class and notes all examples were done in terms of f(x,y). Obviously in h/w, the problem is given as f(x1,x2,x3) - just to confuse me ! Problem statement a- For...
  32. M

    Implicit differentiation dy/dx=xy^2

    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...
  33. E

    Implicit Derivatives - Trigonometry

    Hello hello everyone... I have a problem that I've been trying to figure out for a couple of days now. Its a question off of an assignment, and I have been busting my balls(excuse my french) with no results. HELP would be GREATLY appreciated...lthis is the question at hand: xsin(y) + x^3...
  34. U

    Implicit differentiation? implicit integration?

    We have implicit differentiation: i.e. x^2 + y^2 = 7 -> 2x +2y(dy/dx) = 0. and solve for dy/dx gives you the derivative of y with respect to x However, is there not implicit integration? for terms linear in y, i.e. x^2 + y = 7 -> X^3/3 +int(y) = 7x + K, and solve for int(y) to...
  35. B

    Implicit Differentiation of Cylinder NOT given radius?

    Implicit Differentiation of Cylinder NOT given radius? Homework Statement Question: Digging in his backyard, Dennis accidentally breaks a pipe attached to his water sprinkling system. water bubbles up at a rate of 1 cm^3/s, forming a circular pond of depth 0.5cm in his yard. How quickly is...
  36. P

    Fortran What are Implicit Variables in FORTRAN and How Do They Affect Programming?

    I got a new project from my professor to calculate the form factor of the cavity for his particle detector thing. He told me to get some code from a colleague, decipher it, and use it for the new cavity. The code is in FORTRAN. I've had some programming experience, so it's not so bad, but...
  37. S

    Implicit differentiation and chain rule-

    The question and my workings are attached:
  38. DocZaius

    Is light travel time for event time calculation usually implicit?

    I am beginning a textbook on SR and I have come across the introductory example of disagreement regarding simultaneity. John is in a lab and Mary flies through the lab's corridor on a rocket. The rocket has an antenna. The antenna strikes John's pen in his shirt pocket and creates a spark. 2...
  39. E

    Implicit Differential Equation: dy/dx = xy - y^2

    If dy/dx = xy - y^2 and y(1) = 3, then y(2) is ?
  40. H

    Implicit Differentiation [SOLVED]

    [SOLVED] Implicit Differentiation -4x^2+3xy+4y^3=-328 This is at the point (3,-4) and i am trying to find m Homework Equations The Attempt at a Solution here is my work -4x^2+3xy+4y^3=-328 -8x+3xy'+3y+12y^2y'=0 -8x+3y=-3xy'-12y^2y' -8x+3y=[-3x-12y^2]y'...
  41. H

    What is the error in this implicit differentiation problem at the point (1,3)?

    [SOLVED] Implicit Differentiation [b]-4x^2+3xy+4y^3=-328 This is at the point (1,3) Homework Equations The Attempt at a Solution here is my work -4x^2+3xy+4y^3=-328 -8x+3xy'+3y+12y^2y'=0 -8x+3y=-3xy'-12y^2y' -8x+3y=[-3x-12y^2]y' y'=(-8x+3y)/(-3x-12y^2) plug in x=1,y=3...
  42. O

    Implicit differentiation question

    Find y' = dy/dx for x3 + y3 = 4 Okay, now what's really confusing me is that for the y3 is that you need to use the chain rule for it. When you do, the answer is 3y2(dy/dx). How does that actually work? And if anyone can give me any good advice on any good guidelines on how to properly...
  43. B

    How to Solve Implicit Differentiation Problems with Tan(xy)=xy?

    okay, so i have the problem tan(xy)=xy and i am told to implicitly differentiate in terms of x and y. when i do, i keep getting an indefinite answer. i need help because i know that's not right.
  44. B

    Implicit differentiation of one-parameter family

    Homework Statement Use implicit differentiation to show that the one parameter family f(x, y)=c satisfies the differential equation dy/dx = -f_{x}/f_{y} , where f_{x}=\frac{\partial f}{\partial x} and f_{y}=\frac{\partial f}{\partial y} .Homework EquationsThe Attempt at a Solution Well, my...
  45. A

    How Do You Solve Second Derivatives Using Implicit Differentiation?

    Hi, I need some help with these question, and would appreciate the help. Homework Statement Part 1 Use implicit differentiation to find y'' if 2xy = y^2 Simplify and Leaev in terms of x and y. Part 2 Use implicit differentiation to find y '' if xy + y^3 = 1 Simplify your answer and...
  46. E

    Implicit Differentiation for Tangent Line Equations

    Homework Statement I need to find a tangent line equation but my main problem is isolating actually. sqrt ( 2x + 2y ) + sqrt ( 3xy) = 13 The Attempt at a Solution 0.5 ( 2x + 2y ) ^ -0.5 (2+2y') + 0.5(3xy) ^ -0.5 ( 3 ( y + y' x ) ) = 0 this is where I get stuck
  47. C

    AP calculus, implicit derivatives

    Homework Statement 1. Given the curve x² - xy + y² = 9 (a) Write a general expression for the slope of the curve (b) find the coordinates of the points on the curve where the tangents are vertical (c) at the point (0,3) find the rate of change in the slope of the curve with respect to x...
  48. W

    Implicit function theorem

    Hello all, I've been reading through my textbook about the Implicit function theorem and have come across something in one the examples that I just don't understand: Let F(x,y) = x - y^2 -1, then the partial der. F(a,b) WRT y = -2y, which is 0 only when b = 0. We know the possible...
  49. R

    Implicit differentiation wrt time

    Homework Statement "A lawn sprinkler is constructed in such a way that d\theta/dt is constant, where theta ranges between 45 degrees and 135 degrees. The distance the water travels horizontally is x=v^2sin(2\theta)/32 where v is the speed of the water. Find dx/dt and explain why this lawn...
  50. N

    A few implicit differentiation problems

    1.Use implicit differentiation to find the equation of the tangent line to the curve xy^3+xy=16 at the point (8,1) . The equation of this tangent line can be written in the form y=mx+b 2.For the equation given below, evaluate y^1 at the point(1,-1) . (6x-y)^4+2y^3=2399. 3.Find the...
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