Implicit differentiation Definition and 278 Threads

Homework Statement Its not homework, i have the answer I am just having a hard time wrapping my head around the concept of differentiating implicitly defined functions. the question was: x^3+y^3=3xy, find the equation of the tangent line at the point (3/2,3/2). Homework Equations...

Homework Statement [SIZE="4"] 2x^{3}-3x^{2}y+2xy^{2}-y^{3}=2 Homework Equations The Attempt at a Solution [SIZE="4"] 6x^{2}-(6xy+3x^{2}y')+(2y^{2}+4xyy')-3y^{2}y'=0 y'=\frac{-6x^{2}+6xy-2y^{2}}{-3x^{2}y+4xy-3y^{2}} My text's solution is the same answer but with every every...

I tried deriving this one on my own and I'm just not understanding where the dx/dx term comes from. I'm looking dy/dx. Starting with F(x,y) = 0: \frac{\partial{F}}{\partial{x}}\frac{dx}{dx} + \frac{\partial{F}}{\partial{y}}\frac{dy}{dx} = 0 It seems redundant to say dx/dx when it turns out to...

Use implicit differentiation to find the slope of the tangent line to the curve at the specified point. 3(x^2 + y^2)^2 = 25(x^2 - y^2) ; (2,1) This is where I'm stuck: I know how to get up to the first equation...and I know how to get to the final answer from the second equation, but I...

Homework Statement Find the coordinates of the stationary points on the curve: x^3 + (3x^2)(y) -2y^3=16 Homework Equations Stationary points occur when the first derivative of y with respect to x is equal to zero The Attempt at a Solution I implicitly differentiated the...

I have derivative dx/dt = y(u(t)) * z(u(t)) + u(t) Now, what is dx/du ? I know the chain rule should help, but I am stuck :-(

If, with y a function of x, I have the equation x2-5xy+3y2 = 7, then by implicit differentiation, I get that dy/dx = (2x-5y)/(5x-6y). This equals zero everywhere on the straight line y=(2/5)x except at the origin. This would seem to indicate stationary points everywhere on that line, which is...

Homework Statement z^{3}x+z-2y-1=0 xz+y-x^{2}+5=0 Define z as a function of x, find z'. Homework Equations I guess the two equations above... The Attempt at a Solution Well, I just differentiated the first one with respect to x and got: 3z^{2}xz'+z^{3}3+1=0 z' = \frac{-1-z^{3}{3z^{2}x}...

Homework Statement Find y' in e^(x/y)=x-y 2. The attempt at a solution I tried to differentiate it by changing it so that there would be a natural log (as seen in my attachment). However the end result is not the same as the answer key. How the answer key did it was they used the...

Homework Statement Q 50: The ellipse 3x2 +2y2 = 5 and y3 = x2 HINT: The curves intersect at (1,1) and (-1,1) Two families of curves are said to be orthogonal trajectories (of each other) if each member of one family is orthogonal to each member of the other family. Show that the families of...

Homework Statement x^6 + y^6 = -6 I have to prove that y'' = 30x^4/y^11 Homework Equations The Attempt at a Solution Using implicit differentiation: 6x^5 + 6y^5 dy/dx = 0 6y^5 dy/dx = -6x^5 dy/dx = -x^5/y^5 Quotient Rule: [(y^5)(-5x^4) - (-x^5)(5y^4 dy/dx)] /...

the problem is to find y'' or d2y / d2x the equation is y2 = x2 first i found the first derivative dy/dx = 2x / 2y = x / y then i found the second using the quotient rule and got y'' = (y - x(dy/dx)) / y2 i plugged in y' into y'' and got y'' = (y - (x2/y)) / y2 but then I am...

Homework Statement find the d^2y/dx^2 if y^3 + y = 2 cos x at the point (0,1) Homework Equations The Attempt at a Solution my dy/dx = (-2 sin x)/(3y^2 + 1) I don't know how to find d^2y/dx^2? And when and how will I use the oint (0,1)?

Homework Statement Consider the curve satisfying the equation 2(x+1)^(tanx)=(y^2)cosx+y and find dy/dxHomework Equations (tanx)'=sec^2x (lnx)'=1/xThe Attempt at a Solution I've tried taking the natural log of both sides and then taking d/dx of both sides but something seems to go wrong with...

http://img838.imageshack.us/img838/8007/given01.jpg http://img220.imageshack.us/img220/52/given2r.jpg Actually that should be the square root of -2X

Homework Statement A plane flying with a constant speed of 300 km/h passes over a ground radar station at an altitude of 1 km and climbs at an angle of 30 degrees. At what rate is the distance from the plane to the radar station increasing a minute later? Homework Equations a2+b2=c2The...

I don't think I fully understand implicit differentiation. I have read my textbook and watched many videos, and I think I will get an A on my test on this solely by memorizing the rules, but I would really like to understand this topic. From what I know, you are supposed to use implicit...

Homework Statement x^{3}y + y^{3}x = 30 Homework Equations - The Attempt at a Solution My understanding is that I'm supposed to take the derivative of each side and try to solve for y'. But, I don't know how to treat the y when I am differentiating it, to a power or whatever...

Homework Statement Use implicit differentiation to find dy/dx 2x^3+x^2y-xy^3 = 2 Homework Equations Chain Rule et al. The Attempt at a Solution My questions is this. When deriving something like xy^3, apply the product rule to get 1y^3 + x\frac{d}{dx}y^3 I am confused on...

Homework Statement I tried using D[x = y - y^2, x, NonConstants -> {y}] and it keeps telling me that y - y^2 is not a valid variable.

Homework Statement Q1. using implicit diff to find dy/dx when x^2 y + 6xy^2 = 5x-2 Q2. Find max and min values of y= x^3 -3x^2 -6x + 7 on the interval -3<=x<=5 Q3.Find the exact values of the x coordinate of the points of inflexion on the graph of y = 2x^4 +3x^2 +x +5 Q4. a red car is...

Good afternoon, This is not actually a homework question; it's for self-study. I'm reading a Calculus book, and one of its exercises asks the following: If xnym = (x+y)n+m, show that xDxy = y (where Dxy is the derivative of y with respect to x). The only way I could think of to get the correct...

Question: y6 + 6 (x^2+4)6 = 9 6y5 .dy/dx . 6(x2 + 4)5 . (2x) = 0 6y5 .dy/dx = -6(x2+4)5 .(2x) dy/dx = 6y5 / -6(x2 + 4)5 .(2x) dy/dx = 6y5 / 12x(x2 +4)5 Although the answer is ment to have y5 as the numerator, not 6y5? ------------- Another Q. [Simplifying result from...

Homework Statement So here's a question from my textbook 'Calculus: Concepts and Contexts' 2nd ed. by James Stewart. This is section 3.6 # 54 We have Cartesian coordinates set up with an ellipse at x^2 + 4y^2 = 5 To the right of the ellipse a lamppost (in 2D!) stands at x=3 with...

Homework Statement "Find dy/dx at the given point by using implicit differentiation" x2y + y2x = -2 at (2, -1) and (x+y)3 = x3 + y3 Homework Equations The Attempt at a Solution 1) x2(dy/dx) + y(2x) + y2(1) + 2y(dy/dx)(x) = -2 x2(dy/dx) + 2xy + y2 + 2xy(dy/dx) = -2...

Please go easy on me, 2 days ago I didnt even know what implicit differentiation was. Homework Statement If x tan y − y tan x = 1, use implicit differentiation to determine dy/dx, expressing your answer in the form dy/dx = f(x, y), The Attempt at a Solution Differentiate first...

Homework Statement Calculate the length of the graph/equation: x^(2/3) + y^(2/3) = a^(2/3) The graph is formed as an s.c. asteroid, almost like a diamond. It seems to be some sort of modified unit circle. Homework Equations The length of the graph between x1 and x2 can be described as L=∫...

Homework Statement Given 5y^2 = 4x - 3/4x + 3 Homework Equations is it permissable to say this is equal to y^2 = 4x -3 /5(4x + 3) and then 2y(dy)/(dx) = what the right side equals thru using the quotient rule? I know the answer is dy/dx = 12/5y(4x + 3)^2 but I don't know how to...

Homework Statement Find d2y/dx2 in terms of x and y for the following equation: xy + y^2 = 1 COMPLETELY SIMPLIFY Homework Equations dy/dx The Attempt at a Solution so i get -y/(x+2y) for the dy/dx. When I try to find the 2nd derivative and plug in dy/dx, I get...

Hi there. Well, I wanted to know how to find the second derivatives of a function using implicit differentiation. Is it possible? I think it is. I think I must use the chain rule somehow, but I don't know how... I'm in multivariable calculus since the function I'm going to use could be seen as a...

implicit differentiation help :) again! Homework Statement Use implicit differentiation 1) x/(y-x2)=1 and 2) (y2-1)3=x2-y The Attempt at a Solution 1) x/(y-x2)=1 => [(y-x2)(1)-(x)((1*dy/dx)-2x)]/[(y-x)2]2=0 => y-x2-x(dy/dx)+2x2=[(y-x)2]2 I think I'm going to stop here because I'm pretty...

Homework Statement Find the points (if any) of of horizontal tangent lines on : x2 + xy + y2 = 6 Homework Equations n/a The Attempt at a Solution So far I've concluded that I must find the points at which dy/dx = 0. I've solved for dy/dx and arrived at dy/dx = (-2x-y)/(x+2y)...

Homework Statement If (sqrt x) + (sqrt y) = 11 and f(9)=64 ---> find f '(9) by implicit differentiation The Attempt at a Solution I keep getting lost in my work here... first, taking derivative of both sides: d/dx ((sqrt x) + (sqrt y)) = d/dx (11)...

I just started learning Implicit Differentiation and came across an issue. I took the derivative of the circle function: y2 + x2 = 1 y' = -x / y This all made sense until I solved the circle function for y, which gives: y = \pm\sqrt{1 - x^2} For any x > 1, it's going to be complex. So, does...

Homework Statement Where does the graph of 25x^2 + 16y^2 + 200x - 160y + 400 = 0 have a horizontal tangent line. Homework Equations dy/dx dx/dy or something not sure. The Attempt at a Solution Well I know that a horizontal tangent line would mean the slope is zero...but what...

implicit differentiation help :) Homework Statement Find dx/dy by implicit differentiation (x2+ y)2+ x2+ xy2= 100Homework Equations The Attempt at a Solution I'm trying to use the chain rule to solve it... i got The derivative ofb(x2+ y)2+ x2+ xy2= 100, with respect to x, is 2(x2+...

Let me first say i just learned implicit differentiation (earlier today) and i am also new in general to derivatives. I am finding implicit differentiation difficult but i want to understand it before we go over it in class. Homework Statement This is a example in my book. I have been trying...

Homework Statement find y' given x3+y2+x+y=2 Homework Equations The Attempt at a Solution dy/dx=3x2+2y(y')+1+y' I know that's wrong because my 89 gives it as y'=(-3x2+1)/(2y+1), I don't know how to get there though and what happened to the =2. Thanks

Homework Statement 2XY = Y^2 prove that y''2 = \frac{y^{2}-2xy}{(y-x)^3} EDIT: Sorry, don't know how to insert a space in Latex. Homework Equations The Attempt at a Solution 2y+2x \frac{dy}{dx} = 2y \frac{dy}{dx} \frac{dy}{dx}(2y-2x) = 2y \frac{dy}{dx}= \frac{y}{y-x}...

Homework Statement differentiate: yx = y / sqrt(x2 + y2) Homework Equations The Attempt at a Solution I solved this problem by taking the ln of both sides and then solving. It seems from the context of the problem set that this was supposed to be easier than that. Am I...

Implicit differentiation, what's going wrong!? Hey people can someone point out to me please where I'm going wrong with part B of this question, can't get it to look the answer in the book, d2y/dx2 = -3(x^6/y^7)- 3(x^2/y^3). My answer is listed below under part B section, but i can't...

Homework Statement Find d2y/dx2 for cos y + x2 =12 The first derivative I think is correct but the second I am unsure of, this is Q5 of 10 in an assignment and every other question has been far cleaner and easier making me think that I've missed something. We don't have to use implicit...

Homework Statement Find the equation of a tangent line at the curve at point (-3√3, 1) x^(1/3) + y^(1/3) = 4Homework Equations Point-slope: y-1=m(x-1) The Attempt at a Solution I took the derivative of that equation and resulted in -y^(2/3)/x^(2/3) When I tried plugging in x and y to...

Homework Statement A conical tent must contain 40\pi ft^{3}. Compute the height and radius of the tent with minimal total surface area. (Include the floor material.) Homework Equations 1. \frac{\pi r^{2} h}{3} = 40\pi 2. \pi r \sqrt{r^{2} + h^{2}} + \pi r^{2} = S 3. \frac {dr}{dh} =...

can someone show me step by step how to find dy/dx of y=1/(x+y) using implicit differentiation?

An example of implicit differentation in Stewart, 6th ed, p 883, is given as follows: x^3 + y^3 + z^3 + 6xyz = 1 Differentiating to find dz/dx, 3x^2 + 3z^2(dz/dx) + 6yz + 6xy(dz/dx) = 0 where the product rule was used to differentiate 6xyz with respect to x. Why isn't the...

1. I'm pretty sure I've got this right.. just needing a check. Cheers! 2. x^2+2xy-y^2+x^2=2 3. 2x+2x(dy/dx)+2y-2y(dy/dx)+2x=0 2x(dy/dx)-2y(dy/dx)=-4x-2y dy/dx(2x-2y)=-4x-2y dy/dx=(-4x-2y)/(2x-2y)

Homework Statement Find the points on the lemniscate: 2( x^2 + y^2 )^2 = 25( x^2 - y^2 ) where the tangent is horizontal Homework Equations Horizontal tangent: y' = 0 The Attempt at a Solution I got the correct gradient of y' = [ 50x - 8x^3 - 8y^2 ] / [ (8x^2)y + 50y + 8y^3 ]...

Homework Statement If y= \ln \sqrt{xy} , find the value of dy/dx when y=1 Homework Equations The Attempt at a Solution \frac{dy}{dx} = \frac{1}{\sqrt{xy}} \cdot \frac{1}{2\sqrt{xy}}\cdot (x\frac{dy}{dx}+y) \frac{dy}{dx}=\frac{1}{x} , when y=1

Homework Statement Determine dy/dx xy^-2 = 1 Homework Equations The Attempt at a Solution Here's what I tried: y^-2 - 2xy^-3(dy/dx) = 1 dy/dx = (y - y^3)/2x The answer in the book is y/2x. How do you do it?