Implicit Definition and 537 Threads

Homework Statement What is the integral of: y + x \frac{dy}{dx} The Attempt at a Solution I know that it is xy, after implicit differentiation. However, I cannot get it without prior knowledge of implicit differentiation.

Homework Statement dy/dx = [3(x^2)y - y^2] / [2xy - x^3] Find the x-coordinate of each point on the curve where the tangent line is vertical. Homework Equations original equation is x(y^2) - (x^3)y = 6 The Attempt at a Solution i set the denominator of the deriv. to 0, but i...

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...

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...

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...

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?

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...

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

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

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...

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...

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.

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)

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

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.

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 +...

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}...

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?

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...

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)...

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...

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...

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...

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?

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.

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 =...

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...

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...

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...

(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?

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?

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}}...

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...

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...

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...

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...

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...

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...

The question and my workings are attached:

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...

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

[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'...

[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...

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...

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.

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...

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...

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

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...

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...