Implicit Definition and 537 Threads

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...

Homework Statement find the lines that are (a)tangent and (b)normal to the curve at the given point: x2 - √(3)xy + 2y2 = 5, (√3, 2) Homework Equations dy/dx The Attempt at a Solution i am completely confused about implicit differentiation and the chain rule. I've learned...

Hi all, I was reading a paper in which implicit differentiation was used as follows x \in R, \lambda \in R Given G(x,\lambda) = 0 \frac{\partial G(x,\lambda)}{\partial x} \frac{\partial x}{\partial \lambda} + \frac{\partial G(x,\lambda)}{\partial \lambda} = 0 My doubt is...

Hi, So, I am reviewing Cal III, and I have come across something that I do not understand regarding implicit differentiation with partial derivatives: x^3 + y^3 + z^3 + 6xyz = 1 implicit differentiation of z with respect to x: 3x^2 + 3z^2(dz/dx) + 6yz + 6xy(dz/dx) = 0 *notive the...

How would you find the second derivative of an implicit function? y^2-x^2=16 Heres my attempt: 2y(dy/dx)-2x=0 2y(dy/dx)=2x 2y(dy/dx)/2y=2x/2y dy/dx= x/y This is only the first derivative. I think I'm suppose to plug in dy/dx back into the original equation. Am I on the right track?

Hello, I was just reading about implicit vs explicit finite element solvers and have a question about the difference between them. I understand that the implicit solver has a linear approximation step that is used to force equilibrium. My question is does that make the explicit solver...

Homework Statement Use implicit differentiation to find ∂z/∂x and ∂z/∂y yz = ln(x + z) The Attempt at a Solution I came up with (x+2)/(x+2)(1-xy-yz) Could someone please help me solve this. I know to treat y as a constant and to multiply all the derivatives of z by ∂z/∂x

Homework Statement 2*y + sin(y) = x^4 + 4(x)^3 + (2(Pi) - 5), show that dy/dx = 16, when x = 1. Homework Equations The Attempt at a Solution So I implicitly differentiated it to be dy/dx(2 + cos(y)) = 4(x)^3 + 12(x)^2, and I end up with dy/dx = 16 / (2 + cos (y)) which means that...

||e_i+1|| <= ||e_i||+h||f( (t_i+t_i+1)/2, y_i+y_i+1)/2)-f((t_i+t_i+1)/2, y(t_i+t_i+1)/2))||+O(h^3). I need help about this question.if anybody able to guide me , I be thankful .

Homework Statement Assume that the following equation define the implicit function y=(x). Find the its derivative: x2 + 2xy - y2 = a2 y'=? y''=? Homework Equations \frac{dy}{dx} = -\frac{F_x}{F_y} The Attempt at a Solution so for the first derivative I express that equation as...

Hi, I am working on my differential equations excercises and I encountered 2 problems. First one is, I just wanted to check if I did this implicit differenriation right Homework Statement t^{2} \bullet y +y^{2} = C where is is a constant The Attempt at a Solution My solution is y...

In class we defined convergence as \forall\varepsilon>0\;\;\;\exists\mathrm{N}\epsilon\mathbf{N}\;\;\;\forall\mathrm{n}\geq\mathrm{N}\;\;\;\left|a_{n} \right|<\varepsilon So if a sequence {a_n} of real numbers converge to 0 if for every ε > 0 there is N s.t. |x_n| < ε for n ≥ N... Is the...

Suppose you know that a function g(x,y,z) has a unique, non-degenerate minimum at some point (x_0,y_0,z_0). How could you go about using the implicit function theorem to prove that f(x,y,z) = g(x,y,z) + C h(x,y,z), where C is some constant, has a minimum at some point (x_c,y_c,z_c)? Could we...

Homework Statement Show that the set defined by the equations x + y + z + w = sin(xyzw) x - y + z + w^2 = cos(xyzw) - 1 can be described explicitly by equation of the form (z, w) = f(x, y) near the point (0,0,0,0); find the first partial derivatives of f(x,y) at the point (0,0)...

Homework Statement Can the equation x^2 + y^2 + z^2 = 3, xy + tz = 2, xz + ty + e^t = 0 be solved for x, y, z as C^1 functions of t near (x, y, z, t) = (-1, -2, 1, 0)? Homework Equations The Attempt at a Solution The mixed-partial derivatives matrix I got was: [2x, 2y, 2z, 0]...

Homework Statement Find \frac{\partial\theta}{\partial y} z=rcos\theta x=rsin\theta\cos\phi y=rsin\theta\sin\phi r^2=x^2 + y^2 + z^2 The Attempt at a Solution We know cos\theta=\frac{z}{r}=\frac{z}{\sqrt{x^2 + y^2 + z^2}} So implicit differentiation says to differentiate...

Homework Statement 8x^2-10xy+3y^2=26 2. The attempt at a solution (8)(2x)-(-10x)y'+(y)(-10)+(3)(2y)y'=0 16x+10x(y')-10y+6y(y')=0 y'(10x+6y)+16x-10y=0 y'(10x+6y)=10y-16x y'=(10y-16x)/(10x+6y) y'=(5y-8x)/(5x+3y) I know I'm doing something wrong but I can't see it for...

Homework Statement What is the derivative of x^2 + y^2 = 2y, and find the tangent line to this equation at (1,1) Homework Equations The Attempt at a Solution I get y' = x / (1-y). However, how do I find the tangent line to this? When I plug in the values it divides by zero! (1 /...

"implicit differentiation" if [x][3] * f(x) + [(f(x))][3] + f([x][3]) = 3 and f(1)= 2 find f'(1) NEED HELP REVIEW QUESTION FROM EXAM REVIEW DONT KNOW WHAT TO DO

Homework Statement Use Implicit Differentiation to find y' of the equation 5x^2+ 3xy+y^2=152. The attempt at a solution y'= (-10x-5y)/3x I would like to know if I did this right. I am not very confident in my math sometimes that why I came here. If i did this wrong will you please steer me...

Implicit Function Theorem ...Tricky Proof on matrices!? Homework Statement Implicit Function Theorem ... Tricky Proof on matrices!? Show with the Implicit Function Theorem, that an n x n matrix B, can be solved for as a continuous differentiable function of a matrix A (which is n x n)...

Homework Statement I've got a question more with the structure of how this problem is presented: If x^(sin y) = y^(cos x) Find \frac{dx}{dy}(\frac{pi}{4},\frac{pi}{4}) Homework Equations We have been taught to solve by implicit...

I've been working on this problem for a while and can't see my mistake, in the book the answer is stated as being 3, but I end up getting 13.5. Homework Statement If x^2+3y^2+2y = 10; dx/dt = 2, x=3 and y = -1 find dy/dt The Attempt at a Solution d/dt[x^2+3y^2+2y] = d/dt[10] 3x^2 (dx/dt) +...

Homework Statement Assume the F(x,y,z) = 0 defines z implicitly as a function of x anf y. Show that Homework Equations ∂z/∂x = -(∂F/∂x)/(∂F/∂z) The Attempt at a Solution I know this question is asking about the Implicit function theorem So I start with F(x,y,z) =0 define...

I've began learning some Implicit Functions but graphing them seems to be a problem. I'm using MathGV for graphing. Should I choose 2D or 3D graphs? It's not graphing with 2D, and solving for x or y would be an even bigger problem. For instance, 3(x^2+y^2)^2 = 100xy will graph in 3D but is...

Homework Statement substituting r for y and theta for x as it will be easier to read find dy/dx if r=x^2 tan(2x) I don't know the answer Homework Equations The Attempt at a Solution d/dx (y) = d/dx [x^2 tan(2x)] dy/dx = dx/dx [2x] d/dx [tan (2x)] dy/dx = 2x sec^2...

Homework Statement Find y' Homework Equations The Attempt at a Solution My solution: it's correct?

Homework Statement Find an equation of the tangent line to this curve at the point (1, -2). Homework Equations The Attempt at a Solution 2y' = 3x^2+6x y' = 3x^2+6x y'=3/2x^2+3x y+2=3(x-1) y+2=3x-3 y=3x-5

Homework Statement Homework Equations The Attempt at a Solution

Use Implicit Differentiation to find y" if xy + y - x = 1 so far i got 1y + dy/dx - dx/dx = 1/dx then i did y + y' - 1 = 0 y' = 1-y i don't understand how to get the y" . i don't think i even have y' done right!

Homework Statement Prove that \frac{dy}{dx}=\frac{y}{x} for \sqrt{\frac{x}{y}}+\sqrt{\frac{y}{x}}=10 x is not equal to y which is not equal to 0 The Attempt at a Solution Tried all the normal methods but none seem to work...anyone have any ideas?

Homework Statement Find derivative of y with respect to x. Sin(xy) = Sinx Siny Homework Equations The Attempt at a Solution Use chain rule (product rule for inner function) to differentiate the left. Use product rule to differentiate the right and I get the following...

I have been able to follow how to take the derivative of implicit functions, such as: x^2+y^2-1=0 Differentiating with respect to x 2x+2y\frac{dy}{dx}=0 \frac{dy}{dx}=\frac{-x}{y} Sure it's simple to follow, but I don't understand why the \frac{dy}{dx} is tacked onto the end of...

For couple of days now I've been trying to figure out the implicit function theorem. Especially why we have to be near a point, why can't we be exactly in the point when trying to find out y as a function of x. Let's take an easy equation as an example. Find y=y(x) when f(x,y)=x^2+y^2-1. If...

Homework Statement find dy/dx for x2y+xy2=6 Homework Equations The Attempt at a Solution d/dx (x2y+xy2) = d/dx (6) x2*(dy/dx)+y*2x+x*2y(dy/dx)+2y=0 x2*(dy/dx)+y*2x+x*2y(dy/dx)=-2y (dy/dx)+y*2x+x*2y(dy/dx)=(-2y/x2) (dy/dx)+y*2x+(dy/dx)=(-2y/x2+2xy) I'm not sure what to do...

What is a good book that gives a clear idea of what these theorems are? I am taking differential geometry, and I would like to try and get a better understanding of them. To be honest, my calculus sequence NEVER went over them, so I need to get these ideas under my belt.

Homework Statement Given a continuous parametric function f : R2 -> R3 specifying a 2D surface in 3D space, define a continuous implicit function g : R3 -> R corresponding to the same surface. Homework Equations You’ll likely want to use the infimum function. You can ignore the...

I was working on double integrals when I came across the equation: x^(3/2)=sin(x). There was no noticeable way to isolate the equation for x without having a function of x equal to x. I am wondering how to isolate equations involving logs, sines, etc when it is given in an implicit form. Using...

Homework Statement Consider y = 2a + ax find dy/dx dy/dx = a That is right is it not, as a is treated merly as a constantNow consider this question: Use the substitution y = vx to transform the equation: dy/dx = (4x+y)(x+y)/x² into x(dv/dx) = (2+v)² According to the mark scheme they...