Implicit Definition and 520 Threads

Homework Statement If (1+x^2)(y^2)=1-x^2, show that (\frac{d}{{dx}})^2=\frac{1-y^4}{{1-x^4}} 2. The attempt at a solution http://img294.imageshack.us/img294/7133/calcqn1qd8.gif I have got to this point and tried to simplify the problem with no success ... Have I made an error in my...

Question: Find the co ords of the turning points of y^3 + 3xy^2 - x^3 = 3 Attempt: (differentiate w.r.t. x) d/dx(y^3 + 3xy^2 - x^3) = d3/dx 3y^2(dy/dx) + 3(2xy(dy/dx) + y^2) - 3x^2 = 0 (divide through by 3) y^2(dy/dx) + 2xy(dy/dx) = x^2 - y^2 (take dy/dx as a comon factor) dy/dx(y^2 +...

Homework Statement http://img224.imageshack.us/img224/2459/untitledow9.jpg Homework Equations The Attempt at a Solution See above picture. I'm just curious to see if my method is correct and how exactly would I go about simplifying the answer if indeed it is correct. Thanks...

Homework Statement A spotlight on the ground shines on a wall 14m away. If a dog, 0.5m tall, runs from the spotlight towars the building at a speed of 1 m/s, how fast is the height of the animal's shadow on the building decreasing when the dog is 5 meters from the building? Wrt = with...

I'm trying to understand something that's coming from my Marion & Thornton (4th edition 1995 on p. 264 in a section titled "Conservation Theorems Revisited"). The topic is conservation of energy and introduction of the Hamiltonian from Lagrange's equations. We're told that the Lagrangian...

Is it possible to make a least squares fit with a function given implicitly, because the equation isn't solveable analyticly? Because I had the coupled ODE, \ddot{x} = \omega^2x + 2\omega\dot{y} - C\,\frac{\dot{x}}{\dot{r}} \ddot{y} = \omega^2y - 2\omega\dot{x} - C\,\frac{\dot{y}}{\dot{r}}...

e^x^y = x +y ok i know i am suppost to use the chain rule and the product rule so x+y is 1 +1 if u find the derivatives, but e^x^2 is confusing me, what is u and what is n i think u= e^x^2 and n= y is that possible for n to equal y, this problem is confusing

of 4 cos x sin y =1 here's what i did d/dx 4 cosx sin y)= 1 d/dx 4sinx cosy=0 y'= 4 sinx cosy but the answer is tan x tan y

find y'' (double prime) for x^4+y^4=1

Hi! I've got a question about implicit functions. I have to solve a system f(x,y,z)=0 in the neighbourhood of (1,1,1). I have a problem computing the derivative of an implicit function (x,y)=g(z), whose existence is given by the implicit function theorem when applied to the given function...

Some mathematicians note that their intellectual powers (at least where mathematics is concerned) seem to diminish with age, for instance Hardy. Was this griping a mere excuse for their lack of talent to begin with? Other prodigies appeared to have retained their mathematical fecundity into...

Hi! This is my first post...I've a little question about a mathematical issue I found in the passage from explicit to implicit equations of a dynamical system. How to demonstrate that?? http://pixhost.eu/show_big.php?/share/2007-01-19/doi.jpg Thanks to all

Suppose F(x, y) is C1. F(0, 0) = 0. What conditions on F will guarantee that the equation F(F(x, y), y) = 0 can be solved for y as a C1 function of x near (0, 0) ? would it simply be dF/dy not equal 0 ?

if z was solved in terms of x, y, then when we differenciate d (dz/dx) / dx, are we treating z as a constant or still a function of x, y ?

Hi! I have a problem here that's been bugging me. I was wondering if anyone can give insight into where I'm going wrong implicit differentiation problem 1) (x^2+y^2)/(x+y)=xy-2 find derivitive (dy/dx) at point (-1, -1) I know the basic premise. I used the quotient rule to find the...

the equation x sin (xy) +2x² defines y implicitly as a function of x. assuming the derivative y' exists, show that it satisfies the equation y'x² cos (xy) +xy cos(xy)+sin (xy)+4x = 0. Help needed please. I found the derivative of the first equation is: sin xy + xy cos xy +4x. It's close...

Today I revised my knowledge from multivariable calculus and I found that I couldn't remember the proofs of these two theorems. Then I looked in Rudin, and everything was clear. Except one thing, which probably made me forgot the proofs. There are two weird functions in these two proofs...

Alright I have the question: Find dy/dx by implicit differentiatin ysin(x^2) = xsin(y^2) Basically you jus take the derivative of both sides and solve for dy/dx, but I was unsure whether or not my differentation was right. If someone could just get me started in the right direction for...

I can't get the problem. can anyone help me please. -Find equations for two lines thorugh the origin that are tangent to the curve x^2 - 4x +y^2 + 3 = 0. I found dy/dx=(-x+2)/y and put thta into the point slope equation, and then filled in (0,0) for the point, but couldn't get an...

ok so i did this problem but i wasnt sure if this is correct. y = 8x + 5cos(xy) + 7 dy/dx = 8 + 5(-sin xy)(x dy/dx + y) dy/dx = 8 - (5x) (sin xy) dy/dx - (5y) (sin xy) (5x) (sin xy) dy/dx + dy/dx = 8 - (5y) (sin xy) [(5x) (sin xy) + 1] dy/dx = 8 - (5y) (sin xy) dy/dx = [8 - (5y) (sin...

I have this question in which I know I probably have to use implicit differentiation but I have no idea how to do this can someone give me a hint to get started. all the implicit differentiation problems I have done only have a combination of x and y but this one has x, y and t. find dy/dx...

The problem is as follows: Cartesian and polar coordinates are related by the formulas x = r\cos\theta y = r\sin\theta Determine \frac{\partial r}{\partial x}, \frac{\partial r}{\partial y}, \frac{\partial\theta}{\partial x}, and \frac{\partial\theta}{\partial x}. Differentiate the...

Could someone please make sure I'm doing this right. I want to find the derivative of the logarithm to the base a of x, using implicit differentiation. Let y = \log_{a} x a^y = x \frac{d}{dx} (a^y) = 1 (implicit differentiation) \frac{d}{dx} (e^{\ln a})^y = 1 \frac{d}{dx} (e^{(\ln a)y}) = 1...

Hi there. I've recently come across the Implicit Mapping Theorm in my studies and noticed that there is a condition that the rank of the image must be the maximum possible. I'm not directly seeing why this condition is needed, so I was wondering if anyone could provide me with an example of why...

Were assigned questions regarding implicit differentiation and the second derivative but did not receive a formal lesson so I need some explanations. Example: Find the second derivative x^3 + y^3 = 1 I found this solution on the internet and the answer matches the one in the textbook...

Can anybody give me links to download software that can plot implicit functions like x^2 + xy =9 etc. I have searched the net but all that i have found are shareware demos that expire after a period.I am sure there are freeware plotters of this kind but can't find any.

I need to compute the partials of z with respect to x and y of: xy + z + 3xz^5 = 4 at (1,0). I already showed that the equation is solvable for z as a function of (x,y) near (1,0,1) with the special implicit function theorem, but that's the easy part. Could someone explain to me how to begin...

Consider the curve given by X^2+4y^2=7+3xy a) show that dy/dx=3y-2x/8y-3x b) show that there is a point P with x-cooridnate 3 at which the line tangent to the curve at P is horizontal. Find the y-cooridnate of P. c)find the value of d^2y/dx^2 at the point P found in part (b). Does the curve...

Hello everyone, yet another obscure problem on web work. No examples like this in the book nor did the professor go over it so i was wondering if someone can let me know what exactly they are wanting me to do! Find an explicit or implicit solutions to the differential equation...

Assume that y is a function of x . Find y' = dy/dx for (x^3+y^3)^20 when i solved this i got y'= (20(x^3+y^3)^19 * 3x^2)/(-3y^2) is this correct or am i missing something?

x^2+y^2+r^2-2s=13=0 x^3-y^3-r^3+3s+59=0 How do I find the partial derivatives of x(r,s) or y(r,s) implicitly? I tried implicit differentiation and I got 2 different answers for either. Can someone show me any of the 4 derivatives step-by-step?

Lately, we've been going over these two theorems in class. I have a few questions to put forth. 1) I know that in lower spaces, an inverse of a function exists locally (say around a point G) if it does not attain it's max/min at G (i.e. if f'(G) doesn't equal 0). Now, with the inverse...

The question I'm having trouble with is as follows: Given that siny = 2sinx show that: a) (dy/dx)^2 = 1+3sec^2(y), by differentiating this equation with respect to x show that b)d^2y/dx^2 = 3sec^2ytany and hence that c) coty(d^2y/dx^2) - (dy/dx)^2 + 1 = 0 Part (c) is straight forward and...

Can someone check my answer (I am trying to find the second derivative) for any mistakes? I have looked it over many times, and I've realized that my second derivative is not correct, but I cannot figure out why. Thank you. \sqrt{x} + \sqrt{y} = 1 \frac{1}{2\sqrt{x}} +...

hello everyone I'm stuck! anyone have any ideas? I'm suppose to find dz/dx and dz/dy with implicit differentation. This is calc III! http://img221.imageshack.us/img221/4000/lastscan4ou.jpg

How do I correctly differentiate this using implicit differentiation: xy^1/2 = 1 + x^2y I got to here before I started wondering how I would properly isolate y': ((1/2xy)^-1/2)y + y'x = 2xy + x^2y' How far off the beaten path...

Find \frac{dy}{dx} given cos(y^2) = x^4 Is this correct: 1. cos(y^2) = x^4 2. -sin(y^2) \times 2y \frac{dy}{dx} = 4x^3 3. \frac{dy}{dx} = \frac{4x^3}{-2sin(y^2)}

If you are given the derivative of an implicit function as y' = \frac{y}{2y+x} how would you find all points (x,y) such that the slope at those points is 1/2? Ok so I did: \frac{y}{2y+x} = \frac{1}{2} and got x = 0. So if I substitute x = 0 back into the original equation I get (0...

Implicit Differentiation Problem -- Check my work? I've worked it -- can someone just check my work? Problem: xcosy+ycos=1 My work: [x (d/x)cosy + cosy (d/dx)x] + [y (d/dx)cosx + cosx (d/dx)y] = (d/dx) 1 -xsiny (dy/dx) + cos y - ysinx + cos x (dy/dx) = 0 -xsiny (dy/dx) + cos y...

Doing fine until I reached a trig function where I know I've done the work correctly but the answer does not match up exactly with the one in the back of the book. \sin(x^2y^2)=x I do the work using product and chain rule \cos(x^2y^2)(2xy^2+2x^2yy')=1 2xy^2+2x^2yy' = \frac {1}...

Hello all. I am given the equation (x^3 y^4)^5 = x-y my derivative is 1/ (15x^2 20y^3(x^3y^4)^4)=y' But the book says: y'=(1-15x^14y^20)/(1+20x^15y^19) Where did I go wrong? Thanks so much Chris

f(x,y,z,u,v)=xe^y+uz-\cos v=2 g(x,y,z,u,v)=u\cos y+x^2v-yz^2=1 I need to find u_z. When I try to do it by implicitly differentiating and solving the equation, I get 2 contradictory answers. If I try the formula, i.e. f_z + f_uu_z + f_vv_z = 0 g_z + g_uu_z + g_vv_z = 0 I get an answer...

A spheroid is defined by: x2/a2 + y2/b2 + z2/a2 - 1 = 0 (equation 1) where a and b are the semi-major and semi-minor axes, respectively. If you have any two of x,y,z-values, you can solve for the third, simply by rearranging the above equation: x = +/- sqrt(1 - y2/b2 -...

I have been reviewing Calculus and have tripped up on figuring out to calculate the 2nd partial derivatives of imlicit functions. Kaplan and Spiegel give a cursory treatment to the subject in both of their "Advanced Calculus" books. Simply repeating the methods used to calculate the 1st...

If there is such a thing. I need to find \partial z / \partial x given x + y + z = \cosh xyz. I've never seen the likes of this before and I haven't a clue where to start. Would a reasonable start be to take \partial /\partial x of both sides? If so, it seems like I'm going to end up with an...

Just wondering if I did this right: Here is the question: find \frac{\partial z}{\partial x} of \frac{x^2}{9} - \frac{y^2}{4} + \frac{z^2}{2} = 1 Now I put the \frac{\partial z}{\partial x} on both sides then got. \frac{2x}{9} - 0 + z \frac{\partial z}{\partial x} = 0 So...

Use Implicit Differenciation to find y' f tan(x^2 + y^2) = sec(xy)

Implicit Differentiation...Help! Find \frac{dy}{dx} by Implicit Differentiation: \tan(x - y) = \frac{y}{1 + x^2} \frac{d}{dx} (\tan(x - y)) = \frac{d}{dx} \left( \frac{y}{1 + x^2} \right) \sec^2 (x - y) \cdot \left( 1 - \frac{dy}{dx} \right) = \frac{(1 + x^2) \frac{dy}{dx} - y...

On MathWorld's site, they said that (\frac{\partial{y}}{\partial{x}}){_f} = -\frac{(\frac{\partial{f}}{\partial{x}})_{y}}{(\frac{\partial{f}}{\partial{y}})_{x}} So can this method be used instead of implicit differentiation? Will I get the same result? This seems kind of like a...

hi guys, im a little stuck at the moment trying to answer the follwing calculus question, can anyone help me please. if x=a(theta-sintheta), y=a(theta+sintheta), find dy/dx and d^2y/dx^2 at the point where theta=pi/2. and given that dy.dx=(dx/dy)^-1, find a fomula for d^2x/dy^2 in terms...