Implicit Definition and 537 Threads

Homework Statement Let F: x^2 + y^2 - z^2 + 2xy - 1 = 0 and G: x^3 + y^3 - 5y - 4 = 0. Calculate dz/dx. Note: This is NOT the partial derivative ∂z/∂x. I do not need help in taking the derivative of many polynomials. What I need help in is setting up a Jacobian determinant to evaluate this...

Hi all! In questions having implicit functions, this expression -> "d/dx y^2" often appears in the calculation process. I use the chain rule to convert it to 2y x dy/dx But why can the chain rule be used here? I actually don't understand at all.. Any help is appreciated. Thanks guys!

Hi, I was trying to understand why the chain rule is needed to differentiate expressions implicitly. I began by analyzing the equation used by most websites I visited: e.g. x2+y2 = 10 After a lot of thinking, I got to a reasoning that satisfied me... Here it goes: From my...

I have an implicit function [e.g. x+\frac{ln(y)}{y^2}=0)]. Is there any mathematical trick/technique that can convert this to an explicit function (i.e. y=f(x)) even within certain restrictions and conditions.

So, I understand that implicit differentiation involves derivatives in which x values and y values are mixed up. I've done several implicit differentiation problems a couple sections ago for my math homework, but I pretty just memorized patterns and solved it that way. Now that I'm trying to...

Homework Statement Use the IMPLICIT FUNCTION THEOREM (and not implicit differentiation) to find dy/dx at the point (1,1) when y^5 + x^2*y^3 − y*e^(x^2) = 1.Homework Equations f(x,y)=0 dy/dx = - [f(x)/f(y)] = -[d/dx(f(x,y) / d/dy(f(x,y)]The Attempt at a Solution solving for f(x,y), i brought the 1...

Here is the question: Here is a link to the question: Derive Trig Function? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

Got a little problem here, just want to make sure what I'm doing is right because it's a little different from anything I've done that is using the same formula initially. So there's a sphere denoted as \(\Omega\): $$x^2+y^2+z^2=R^2$$ and its cut by two planes \(z=a\) & \(z=b\) where...

Homework Statement Use implicit differentiation to find y' given y/(x-y) = x^2+1.Homework Equations The Attempt at a Solution Hi, I'm doing an online course for Calculus 12, and I have been struggling with Implicit Differentiation. I am hoping someone could maybe help me. Thanks. I'm not...

Hi, I'm doing an online course for Calculus 12 and I have been struggling with Implicit Differentiation, hoping someone could maybe help me. Thanks. I'm not positive I'm doing this right but maybe someone can point me in the right direction, this is what I have so far y/(x-y) = x^2+1...

The question, from Edward's Advanced Calculus (which is becoming a rather frustrating book), asks if the following surface can be represented as a function of ##z(x,y)## near the point ##(0,2,1)##: xy - ylog(z) + sin(xz) = 0 Naturally, this should invite me to use the Implicit Mapping...

Homework Statement For the curve x2+3xy+y2 = 5 show that \frac{dy}{dx} =- \frac{2x+3y}{3x+2y} Homework Equations N.A. The Attempt at a Solution 2x + 3xy + 2y\frac{dy}{dx} = 0 3x + 2y \frac{dy}{dx} = -2x+ 3y ∴ \frac{dy}{dx} =- \frac{2x+3y}{3x+2y} have I done this correctly?

Homework Statement e^y = x(y-1) answer must be in implicit form Homework Equations The Attempt at a Solution I literally have no idea how to do this problem. I have the answer, but that's it. The answer is dy/dx(e^y) = x(dy/dx) + y - 1

Homework Statement f(x) = f(x_1,...,x_N) : R^N \mapsto R has continuous partial derivatives. Assume that for a point a in R^N , \frac{\partial f}{\partial x_i}(a) \neq 0 for all i = 1...N. The implicit function theorem says that near a, the equation f(x) = f(a) can be used to express each...

So, as the title may have given away, I'm trying to figure out implicit differentiation in the multiple variable context. I thought a good practice would be the law of cosines, aka c^2 = a^2 + b^2 - 2abcosθ. So I'm trying to find ∂θ/∂a, ∂θ/db, ∂θ/dc. I tried solving for θ and then taking...

Homework Statement Use implicit differentiation to find an equation of the tangent line to the curve at the given point. x^2+y^2=(2x^2+2y^2-x)^2 @ (0,(1/2)) Homework Equations The Attempt at a Solution So, I don't have a problem differentiating this. Which I get...

Homework Statement R=1/(.55/c+.45/h) find partial equations respect to c. and respect to h use implicit function differentiation of the reciprocal of R to answer what is the differential change in R when c=20 h=30 and c changes to 21 Homework Equations is there any way to make R...

why is thermal analysis done in implicit scheme

Homework Statement Calculate the derivative with respect to x: x/y + y/x = 2yHomework Equations n/a The Attempt at a Solution I end up getting the right answer, but what I want to know is how to isolate dy/dx to one side after implicitly differentiating. I have tried differentiating the LHS...

Homework Statement The P(a,b) be a point on the curve √x + √y = 1. Show that the slope of the tangent P is -√b/a Homework Equations ? The Attempt at a Solution Apparently this is an implicit differentiation problem, however we haven't learned or discussed implicit...

Say you have x^2+y^2=100. why can't you just solve for y, so y=+- √(100-x^2) then use the chain rule to find the derivative. so y'= +- x/√(100-x^2). Then you can just deduce that y'= -x/y. What is the point of adding all the dy/dx in the equation? Seems like it just complicates it.

Hello, Today did me and my friend talked of derivate and he asked about some help. Then he asked me is it possible to derivate $y^3+5x^2=5x-2y$ and i was clueless how i derivate that. Is this difficoult to derivate?is it possible to do it?

Hello! As of right now (10:13 PM), I've tried 9 combinations of points to solve this problem. It's a WebWork-based problem that's due in about an hour in a half. Any help would be very, very appreciated. Homework Statement I was given this equation: ##ln(2y) = 2xy## and was asked to find...

Homework Statement I'm reviewing physics using Feynman's Lectures, and I'm finding that he frequently uses implicit differentiation in his lessons. This is unfortunate for me because I never got the hang of it beyond the simplest cases. I'm currently going through the proof that the...

Homework Statement Use implicit differentiation to find dy/dx. Homework Equations xey - 10x + 3y = 0 The Attempt at a Solution = [xey + ey(y)'] - (10x)' + (3y)' = 0 = xey + ey(y') - 10 + 3(y') = 0 = y' (ey + 3) = 10 - xey = y' = 10 - xey/ ey + 3y However, my book says the answer: 10 -...

Hi all, In studying the eigenvalues of certain tri-diagonal matrices I have encountered a problem of the following form: {(1+a/x)*2x*sinh[n*arcsinh(x/2)] - 2a*cosh[(n-1)*arcsinh(x/2)]} = 0 where a and n are constants. I'm looking to find n complex roots to this problem, but isolating x...

Homework Statement The equations ##2x^3y+yx^2+t^2=0##, ##x+6+t-1=0## implicitly define a curve $$f(t) = \begin{pmatrix} x(t)\\y(t) \end{pmatrix}$$ that satisfies ##f(1)=\begin{pmatrix} -1\\1 \end{pmatrix}.## Find the tangent line to the curve when ##t=1##. Homework Equations The...

Homework Statement I have a question. How in general would one differentiate a composite function like F(x,y,z)=2x^2-yz+xz^2 where x=2sint , y=t^2-t+1 , and z = 3e^-1 ? I want to find the value of dF/dt evaluated at t=0 and I don't know how. Can someone please walk me through this?Homework...

Equation: eysinx=x+xy I took the derivative of both sides. For the side with eysinx, I used the product rule and chain rule to get: ey*cosx + ey*sinx*y' For the side with x+xy, I used the sum and product rule to get 1+y+xy' So my resulting equation is: ey*cosx + ey*sinx*y'=1+y+xy', which...

1. Given that y^{2}-2xy+x^{3}=0, find \frac{dy}{dx} 2. (no relevant equations other than the problem statement) 3. So, I solved it like this, \frac{dy}{dx}y^{2}-2xy+x^{3}=0 2y\frac{dy}{dx}-2+3x^{2}=0 Solving for dy/dx I got... \frac{dy}{dx}=\frac{-3x^{2}+2}{2y}...

Okay so, I am having trouble figuring out what exactly to do in implicit differentiation and usage of the chain rule. Like, I keep getting the wrong answer somehow. See, from what I understand you have to find the derivative of both sides then use the chain rule or something and then solve for...

Hello, I have recently started a little implicit differentiation and I have seen DEs before but I know that I still need to work on my differentiation and integration a little more before I am ready to tackle those. Anyway, I wish to ask, what distinguishes implicit differentiation from a...

Homework Statement I need to use implicit differentiation to find the derivative of y=sin(x+y). Homework Equations The Attempt at a Solution This is what I did: y=sin(x+y) y'=(sin(x+y))' y'=(1+y')(cos(x+y)) (by the chain rule) Now, what do I do? Is this correct...

1. y = sinxy Homework Equations 3. this was my attempt d/dx = (cosxy)(sinxy(d\dx))+(xy(d/dx) im getting stuck. i don't think I am starting it right. any suggestions.

Hello, I often encounter some confusion. For example, we have the equation for a circle of radius one given by: x2+y2=1 Now we can't express this as a function in R2 because it's a relation. however, we can still find derivatives like dy/dx or dx/dy using implicit...

Hi, The final step of solving a separable ODE is to find a function, f, defined implicitly by a relation G(y) = H(x). Say G(y) isn't defined at y = a and H(x) isn't defined at x = b, it appears to me that when rearranging such a relation to put y in terms of x, the point at which G(y) isn't...

Hello, I am sorry. I apologize for my poor English. [ Implicit assumption of CMBR? ] It is not certain whether this kind of experiment has already been conducted. Still, it need be tested whether the wavelength distribution of 3000k radiation cooling down to 2.7K is completely identical to...

Hello everyone, I have an implicit equation: -155.034 x^4 ×sin(377 t) = 0.0524166 x^6 × cos^{1.414}(-377t)-(0.0581964+0.0442696 i) x ×cos^4(377 t)+7.09332 cos^5(377 t) I would like to create a plot of this function using Mathematica, but I am not very proficient with this software, and...

Homework Statement Verify that the indicated expression is an implicit solution of the given first-order differential equation. Find at least one explicit solution y=∅(x) in each case.Homework Equations \frac{dX}{dt}=(X-1)(1-2X); ln(\frac{2X-1}{X-1})=t The Attempt at a Solution I know I need...

I am trying to understand the role of the Jacobian in the Implicit Function Theorem. However, I have had a hard time finding any discussions that use the Jacobian and are accessible for my level. http://mathworld.wolfram.com/ImplicitFunctionTheorem.html has been the best thing I have found...

Homework Statement Let f(x,y) = xe^{x^2 + y^2} + y^3 + cos x a) Show there exists a differentiable function \phi(y) such that x = \phi(y) solves f(x,y) = 1 in some neighborhood of (0,0) in R^2. (Meaning (x,y) satisfies f(x,y) = 1 for (x,y) near (0,0) if and only if x = \phi(y)) Prove your...

Homework Statement I'm trying to solve the derivative of this equation: 1-(x*arcsin(x))/√(1-x^2 ) I've straight away disregarded the 1 as it will be 0 so I'm left with -(x*arcsin(x))/√(1-x^2 ). The Attempt at a Solution I've applied the quotient rule and labelled U= -x*arcsin(x) and...

Homework Statement I'm try to implicitly differentiate the function: xlny+√y=lnx The Attempt at a Solution And I got to the stage where I have: dy/dx = (1/x-lny)/(x/y+1/(2*√y)) which is where I have no idea on how to clean this up. Could someone please explain to me how to simplify a...

Hi everyone, I do economics but am very poor at Math. I had a specific and perhaps silly question about the implicit function theorem, but will be grateful for an urgent response. Suppose we have a function, U(x, y). x and another variable z are linearly related so the function can also...

for each of the following maps f: ℝ2-->ℝ3, describe the surface S = f(ℝ2) and find a description of S as the locus of an equation F(x,y,z) = 0. Find the points where \partialuf and \partialvf are linearly dependent and describe the singularities of S(if any) at these points f(u,v) = (2u + v...

So I have to determine whether the set S = {(x,y): F(x,y) = 0} is a smooth curve, draw a sketch, examine the nautrue of ∇F = 0. Near which points of S is S the graph of a function y = f(x) and x = f(y) F(x,y) = (x2+y2)(y-x2-1) Attempt: So it is the union of a point and the parabola y = 1+x2...

Homework Statement Find an equation of the tangent line to x^3 + y^3 - 6xy = 0 at the point ((4/3), (8/3)) Homework Equations I got y = -(8/5)x + (24/5). Is this correct? The Attempt at a Solution Lots of algebra involved. Sorry. but I'd rather not type it. I take the derivative of...

Homework Statement Find dy / dx for sqrt(xy) = x - 2y. Homework Equations I don't know how to simplify [(xy' + y) / 2sqrt(xy)] = (1 - 2y') to y' = [- y + 2sqrt(xy)] / [x + 4sqrt(xy)]. The Attempt at a Solution I do everything Wolfram Alpha does here...

So I'm asked to determine near which points of R^3 can we solve for ρ, δ, θ in terms of x,y,z: x = ρ sinδ cosθ y= ρ sinδ sinθ z= ρcosδ so the spherical co-ordinates using IFT. Attempt: Ok so in order to determine solutions, I need to first find where the determinant of the freceht...

Investigate the possibility of solving x2-4x+2y2-yz = 1 for each of its variables in terms of the other two near the point (2,-1,3). Attempt: Ok so using the IFT I was able to determine that I can only slze for y,z. But in the question they ask me to solve for y and z. z was not problem, but...