Implicit differentiation Definition and 279 Threads

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...

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...

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...

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?

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

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)}

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}...

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...

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)

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...

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:

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'=...

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...

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...