Implicit Definition and 537 Threads

Homework Statement find the d^2y/dx^2 if y^3 + y = 2 cos x at the point (0,1) Homework Equations The Attempt at a Solution my dy/dx = (-2 sin x)/(3y^2 + 1) I don't know how to find d^2y/dx^2? And when and how will I use the oint (0,1)?

Homework Statement Consider the curve satisfying the equation 2(x+1)^(tanx)=(y^2)cosx+y and find dy/dxHomework Equations (tanx)'=sec^2x (lnx)'=1/xThe Attempt at a Solution I've tried taking the natural log of both sides and then taking d/dx of both sides but something seems to go wrong with...

Hi, I am trying to write a code for an equation which looks like this: \frac{\partial{y}}{\partial{t}}=f(x,y,t) -y(x^{n+1}-x^{n}) where n is the time step number. I have no idea how I can go on about solving (approximating the solution) to this problem. Any hints would be appreciated...

http://img838.imageshack.us/img838/8007/given01.jpg http://img220.imageshack.us/img220/52/given2r.jpg Actually that should be the square root of -2X

Homework Statement 2x^3 - 8xy + y^2 = 1 Homework Equations The Attempt at a Solution d2x^3/dx - d8xy/dx + dy^2/dx = d1/dx 6x^2 -8(y) + dy/dx(-8x) + 2y(dy/dx) = 0 6x^2 - 8y -8x(dy/dx) + 2y(dy/dx) = 0 I am stuck and can't seem to go further. Someone help?

Homework Statement A plane flying with a constant speed of 300 km/h passes over a ground radar station at an altitude of 1 km and climbs at an angle of 30 degrees. At what rate is the distance from the plane to the radar station increasing a minute later? Homework Equations a2+b2=c2The...

I don't think I fully understand implicit differentiation. I have read my textbook and watched many videos, and I think I will get an A on my test on this solely by memorizing the rules, but I would really like to understand this topic. From what I know, you are supposed to use implicit...

Homework Statement x^{3}y + y^{3}x = 30 Homework Equations - The Attempt at a Solution My understanding is that I'm supposed to take the derivative of each side and try to solve for y'. But, I don't know how to treat the y when I am differentiating it, to a power or whatever...

When solving differential equations numerically with finite difference methods, textbooks get to the point of solving: A psi_(n+1) = B psi_n (with A, B some matrices, typically complex conjugate of each other) and advise on using LU decomposition to do so. My question is, why not...

Implicit => inverse function theorem (urgent due to exam, please help) Homework Statement Prove the inverse function theorem, knowing the implicit function theorem. Homework Equations The statements of both theorems... Can't think of much else. The Attempt at a Solution...

Homework Statement Stewart Calculus (6E) 3.6 question #26 Using implicit differentiation, find the equation of a tangent line to the curve at the given point. x^2+2xy-y^2+x=2 Through point p(1,2) I just want to know if I am doing this correctly. Homework Equations The Attempt at a Solution...

Homework Statement Use implicit differentiation to find dy/dx 2x^3+x^2y-xy^3 = 2 Homework Equations Chain Rule et al. The Attempt at a Solution My questions is this. When deriving something like xy^3, apply the product rule to get 1y^3 + x\frac{d}{dx}y^3 I am confused on...

Faraday's law has an integral and a differential version: curl \mathbf{E} = - \frac{\partial \mathbf{B}}{\partial t} \mbox{ and } \oint_{C} \mathbf{E} \cdot d \mathbf{l}=- \frac{d}{dt} \int_{S} \mathbf{B} \cdot d \mathbf{S} When I use the differential version I always have a constant of...

Homework Statement "Determine whether the equations on the right define implicit functions of x. For those which do, determine whether they are implicit solutions of the differential equations on the left." e^(x-y) + e^(y-x)(dy/dx) = 0, e^(2y)+e^(2x) = 1 The Attempt at a Solution Apologies...

Hi, this is a very basic question. I want to know why are implicit functions used, when the purpose of functions is to calculate the independent variable. For example, why would someone write ay + bx + c = 0 as a "straight line function" (sorry for the possible abuse of language, I don't...

I'm having some trouble grasping the implicit function theroem in some cases. Here's one of them. Homework Statement Show that there exist a C2 function y(x) in some neighbourhood of 0 such that y(0) = 0 and y(x)3 + 3y(x) = x Find y'(0) and y''(0) Homework Equations The implicit function...

Homework Statement This is the solution to an IVP, and the question asks how the function behaves as x Approaches infinity...

Homework Statement I tried using D[x = y - y^2, x, NonConstants -> {y}] and it keeps telling me that y - y^2 is not a valid variable.

Homework Statement The implicit Euler method is yn = yn-1 + hf(xn,yn). Find the local truncation error and hence show that the method is convergent. Homework Equations The Attempt at a Solution I found the error to be ln = (-h2/2)y''(xn-1) + O(h3). For convergence I am up to...

Homework Statement Q1. using implicit diff to find dy/dx when x^2 y + 6xy^2 = 5x-2 Q2. Find max and min values of y= x^3 -3x^2 -6x + 7 on the interval -3<=x<=5 Q3.Find the exact values of the x coordinate of the points of inflexion on the graph of y = 2x^4 +3x^2 +x +5 Q4. a red car is...

Good afternoon, This is not actually a homework question; it's for self-study. I'm reading a Calculus book, and one of its exercises asks the following: If xnym = (x+y)n+m, show that xDxy = y (where Dxy is the derivative of y with respect to x). The only way I could think of to get the correct...

Spivak: Calculus on Manifolds, p. 42: Assuming "differentiating f(x,g(x)) = 0" means differentiating f \circ h, where h : (-1,1) \rightarrow \mathbb{R}^2 \; | \; x \mapsto (I(x),g(x)), I(x) = x and setting the result identically equal to zero, we have 2x+2g(x) \cdot g'(x) = 0, as...

Homework Statement If x(u^2) + v=(y^3), 2yu - x(v^3)=4x. Find a) du/dx and b) dv/dx Homework Equations The Attempt at a Solution Not sure if I am supposed to differentiate as is, or try and write u and v as functions of x and y. The answer is supposed to be: a)...

Homework Statement Even though these questions are economics, it's all just applied mathematics. See attached questions Homework Equations The Attempt at a Solution 1)I assume we just take the first derivative of y w.r.t to p? Since x is constant the optimum value of y will...

Homework Statement I am currently working through the problems in Edwards book "Advanced Calculus of Several Variables". This is the problem (1.9 page 171): Show that the equation z3 + ze(x+y) + 2 = 0 has a unique solution z=f(x, y) defined for all (x,у) an element of R3. Homework...

"Show that the given equation is an implicit solution of the given differential eqn" Homework Statement Show that the given equation is an implicit solution of the given differential equation - y2 - 1 - (2y + xy)(y-prime) = 0 y2 - 1 = (x + 2)2Homework Equations y2 - 1 - (2y +...

Question: y6 + 6 (x^2+4)6 = 9 6y5 .dy/dx . 6(x2 + 4)5 . (2x) = 0 6y5 .dy/dx = -6(x2+4)5 .(2x) dy/dx = 6y5 / -6(x2 + 4)5 .(2x) dy/dx = 6y5 / 12x(x2 +4)5 Although the answer is ment to have y5 as the numerator, not 6y5? ------------- Another Q. [Simplifying result from...

Homework Statement So here's a question from my textbook 'Calculus: Concepts and Contexts' 2nd ed. by James Stewart. This is section 3.6 # 54 We have Cartesian coordinates set up with an ellipse at x^2 + 4y^2 = 5 To the right of the ellipse a lamppost (in 2D!) stands at x=3 with...

Hey folks I'm experimenting with symplectic integrators and I'm trying to figure out how to deal with fourth order implicit Runge-Kutta methods as shown here (symplectic version second link). http://en.wikipedia.org/wiki/Runge%E2%80%93Kutta_methods#Implicit_Runge.E2.80.93Kutta_methods...

Homework Statement "Find dy/dx at the given point by using implicit differentiation" x2y + y2x = -2 at (2, -1) and (x+y)3 = x3 + y3 Homework Equations The Attempt at a Solution 1) x2(dy/dx) + y(2x) + y2(1) + 2y(dy/dx)(x) = -2 x2(dy/dx) + 2xy + y2 + 2xy(dy/dx) = -2...

Please go easy on me, 2 days ago I didnt even know what implicit differentiation was. Homework Statement If x tan y − y tan x = 1, use implicit differentiation to determine dy/dx, expressing your answer in the form dy/dx = f(x, y), The Attempt at a Solution Differentiate first...

Homework Statement An implicit equation for the plane passing through the point (-2,5,-5) that is perpendicular to the line L(t) = <5+2t,3,4> is ...? Homework Equations a(x-x0) + b(y-y0) + c(z-z0) = 0 The Attempt at a Solution So in order to find the equation of the plane I would...

Homework Statement I'm trying to find the center of mass of the region (x²+y²)² =2xy in the first quadrant, but I got stuck. The Attempt at a Solution What I did is make the substitution x = r cos(t), y = r sin(t), which gives the equation r^{4}=2r²cos(t) sin(t), so r² = sin(2t)...

In short, I need to know how do you do them. I missed class, and our textbook is so bad that it might as well be written in a foreign language. I understand how to do dy/dx of an equation not in the form y =... ex. y^2 = x^3 + 2x + 5, (y'=(3x^2 +2)/2y) for example, but how would you take the...

Homework Statement The original function is given as such: y = 13 arctan(\sqrt{x}) Homework Equations The Attempt at a Solution I went ahead and changed it into: tan(\frac{y}{13}) = \sqrt{x} I thought it would be simpler this way. So now I differentiate...

I am trying to solve set of implicit differential equations. But first...i need to find out the consistent initial conditions for my problem( initial condition for derivative). that's why i am using 'decic' built-in function of matlab. But facing following problem. My set of differential...

Homework Statement Given 5y^2 = 4x - 3/4x + 3 Homework Equations is it permissable to say this is equal to y^2 = 4x -3 /5(4x + 3) and then 2y(dy)/(dx) = what the right side equals thru using the quotient rule? I know the answer is dy/dx = 12/5y(4x + 3)^2 but I don't know how to...

I have a implicit differential equation Re(u*ux-u^2)=0 ( It was larger equation but i simplified it here). I wrote down my function in m.file as follows: function Z=fun_imp(x,u,ux); Re=25; Z=0; Z=Re*(u*ux-2*u); Before going to solving differential equation to find out consistent...

Implicit Function Theorem I've been having a lot of trouble understanding the statement of the theorem and its proof, so I would like to see if I did the following question below correctly. The problem Let f : R² → R be given by f(x,y,z) = sin(xyz) + e^[2x + y(z - 1)]. Show that the level set...

I've been having a lot of trouble understanding the statement of the theorem and its proof, so I would like to see if I did the following question below correctly. The problem Let f : R² → R be given by f(x,y,z) = sin(xyz) + e^[2x + y(z - 1)]. Show that the level set {f = 1} can be solved as...

Homework Statement Find d2y/dx2 in terms of x and y for the following equation: xy + y^2 = 1 COMPLETELY SIMPLIFY Homework Equations dy/dx The Attempt at a Solution so i get -y/(x+2y) for the dy/dx. When I try to find the 2nd derivative and plug in dy/dx, I get...

[Solved]Implicit Derivative of this Function Homework Statement Find the implicit Derivative of this function: 1/x+1/y=1 Homework Equations Chain Rule, Quotient Rule ... ? The Attempt at a Solution 1/x-(y'/y^2)=1 (y'/y^2)=1-1/x y'=1/y^2-y^2/x The answer seems to be...

Hi there. Well, I wanted to know how to find the second derivatives of a function using implicit differentiation. Is it possible? I think it is. I think I must use the chain rule somehow, but I don't know how... I'm in multivariable calculus since the function I'm going to use could be seen as a...

implicit differentiation help :) again! Homework Statement Use implicit differentiation 1) x/(y-x2)=1 and 2) (y2-1)3=x2-y The Attempt at a Solution 1) x/(y-x2)=1 => [(y-x2)(1)-(x)((1*dy/dx)-2x)]/[(y-x)2]2=0 => y-x2-x(dy/dx)+2x2=[(y-x)2]2 I think I'm going to stop here because I'm pretty...

Homework Statement Find the points (if any) of of horizontal tangent lines on : x2 + xy + y2 = 6 Homework Equations n/a The Attempt at a Solution So far I've concluded that I must find the points at which dy/dx = 0. I've solved for dy/dx and arrived at dy/dx = (-2x-y)/(x+2y)...

Homework Statement If (sqrt x) + (sqrt y) = 11 and f(9)=64 ---> find f '(9) by implicit differentiation The Attempt at a Solution I keep getting lost in my work here... first, taking derivative of both sides: d/dx ((sqrt x) + (sqrt y)) = d/dx (11)...

I just started learning Implicit Differentiation and came across an issue. I took the derivative of the circle function: y2 + x2 = 1 y' = -x / y This all made sense until I solved the circle function for y, which gives: y = \pm\sqrt{1 - x^2} For any x > 1, it's going to be complex. So, does...

Homework Statement Where does the graph of 25x^2 + 16y^2 + 200x - 160y + 400 = 0 have a horizontal tangent line. Homework Equations dy/dx dx/dy or something not sure. The Attempt at a Solution Well I know that a horizontal tangent line would mean the slope is zero...but what...

Homework Statement Find \partial x / \partial z at the point (1, -1, -3) if the equation xz + y \ln x - x^2 + 4 = 0 defines x as a function of the two independent variables y and z and the partial derivative exists. Homework Equations The Attempt at a Solution x + y/x \partial x...

implicit differentiation help :) Homework Statement Find dx/dy by implicit differentiation (x2+ y)2+ x2+ xy2= 100Homework Equations The Attempt at a Solution I'm trying to use the chain rule to solve it... i got The derivative ofb(x2+ y)2+ x2+ xy2= 100, with respect to x, is 2(x2+...