Implicit Definition and 537 Threads

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...

Find y'' by implicit differentiation x^4+y^4=1 i found that y'=-x^3/y^3 y''=[(y^3)(-3x^2)-(-x^3)(3y^2)(y')]/(y^3)^2 y''=[-3x^2(y^3)-(-x^3)(3y^2)(-x^3/y^3)]/y^6 then i am stuck...please help...thanks

What would be the best way to check the result of implicit differentiation with a TI calculator?

How would you check your answer using a Ti86 for implicit diferentiation problems? I was looking through some source code at ticalc.org and found this tidbit for an implict differentiation section: (after given a point x and y, with function F1) If der1(F1,y)==0 [exit] else...

Hi, here is my problem. I think it has something to do with me not completely understanding implicit differentiation. I have to find \frac{dy}{dx} of x^2+5yx+y^5=8 To do this, I differentiated the x^2 as 2x then I used the product rule to differentiate 5xy into 5y + \frac{dy}{dx} * 5x. I...

Hey all. There's a question I seem to be stuck on involving implict differentiation. Here it is: The curve called a bicorn has the equation (x^2+8y-16)^2=y^2(16-x^2) Verify by implicit differentiation that its tangent lines at the points (0,4) and (0,\frac{4}{3}) are horizontal. Do by...

i am working on a homework assignment. it's easy, or, so i think... Given. 3x^2 - xy^3 + sin(x^3 - y) = 4 Find \frac{dy}{dx} not a problem. i ended up with \frac{dy}{dx} = \frac {6x - y^3 + 3x^2 cos(x^3 - y)}{3xy^2 + cos(x^3 - y)} using implicit differention. now...

Help with Implicit Differentiation Hello all If we are given \cos xy = 2x^2 - 3y find \frac {dy}{dx} So the derivative of \cos xy is - sin(xy)(x)(\frac{dy}{dx} + y) The derivative of the RHS is 4x - 3 \frac {dy}{dx} Hence \-sin(xy)(x)\frac{dy}{dx} + y = 4x - 3 \frac...

Say we have two functions of x, v and y, such that v=x+y. How can I find v'?

Hello all Given: x^2 + xy + y^2 - 7 = 0, solve for y using the quadratic forumula. Then find dy/dx at P(1,2) from a function of the form f(x). My solution: y = -x (+/-) sqrt( x^2 - 28) / 2. I am not sure if this is correct. After solving for y, do you have to implicitly take the...

Find dy/dx by implicit differentiation. (Meaning find the derivative of y.. so y' = ??) cos(x-y)=xe^x Please help and show step by step.. the final answer should be.. y' = 1 + [(e^x)(1+x)]/[sin(x+y)] Thanks a bunch. :smile:

taking derivitive of 2xy^2+xy=y split up to using product rule 2x----2 y^2---2y\frac{dy}{dx} 4yx\frac{dy}{dx}+2y^2+y+x\frac{dy}{dx}=\frac{dy}{dx} \frac{dy}{dx} (4x+x-1)=-2y^2-y \frac{dy}{dx}= \frac{-2y^2-y}{4xy+x-1} i am trying to figure out the slope of the equation...

Please Help! Ok, I am having problem with an Implicit differentiation problem... Two tangent lines to the hyperbola 9x^2 - y^2 =36 intersect at the y-axis. Use implicit differentiation to find the points of tangency. Ok so i implicitly differentiated this function and i came up with y'=...

Hi all: How would you find the second derivative of 2x^3 - 3y^2 = 8? I know the first derivative is x^2 / y. Would I use the quotient rule, or would I use some type of substitution and then use the product rule? Any help is greatly appreciated! Thanks

First off, I must say I truly enjoy these forums, though I tend to shy away from Calculus. Calculus and I just don't seem to get along, which is strange since I really enjoy other forms of math. On to the questions. Note, these 3 are the ones I just can not seem to work through on an...

Hello all, Can somebody give a 'simple to understand' proof for the 'Implicit Function Theorem' and the 'Inverse Function Theorem',their significance, applications and some examples. I have tried some books on Multivariable calculus, but in vain... :cry:

find the turning points on the curve with equation y^3 + 3xy^2 - x^3 = 3 I'm confused bout the 3xy^2 mostly, i kno that xy goes to (y+x dy/dx) but not sure what 2 do bout the power...

My TA did not get the chance to go over this problem. I know that I'm supposed to differentiate both sides of the equation. But I have not the slightest idea what to do after that. I was told that I am supposed to get out 4 points that lie on the ellipse and the sides of the box are tangent...

Here is the problem: Find the equation of the line which is tangent to the curve at the point (1,3): 8x^3y^2 + x^2y^5 + 6 = 4y^4 - 3x^4 Here is what I've done so far (I'm stuck now): (24x^2)(y^2) + (8x^3)(2y dy/dx) + (2x)(y^5) + (x^2)(5y^4 dy/dx) = (16y^3 dy/dx) + 12x^3 Where do...

As part of proving that d/dt <p> = <-Del V> you have to use the fact that < dp/dt> = 0 when p is not an explicit function of time. I'm not clear on what this means. Any insights to share? From classical mechanics, if there is a potential V = -k/r then there will be a force on a particle...

Hi. I'm taking a Calculus course right now and I simply cannot understand Implicit Differentiation or the Related Rate problems. My textbook does not do a good job explaining it. It is a very accelerated class and I cannot get it and I need to know it in two days for a mid term. I just don't...

Can u please give me an example of a problem that use implicit differentiation to find the derivative of an inverse function and of relations. Plz also explain to me what relation means in this case. Thanks also please give me an example that use the definite integral to compute accumulated...