Implicit differentiation Definition and 279 Threads

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 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.

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...

(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?

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}}...

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...

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...

The question and my workings are attached:

[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 "A lawn sprinkler is constructed in such a way that d\theta/dt is constant, where theta ranges between 45 degrees and 135 degrees. The distance the water travels horizontally is x=v^2sin(2\theta)/32 where v is the speed of the water. Find dx/dt and explain why this lawn...

1.Use implicit differentiation to find the equation of the tangent line to the curve xy^3+xy=16 at the point (8,1) . The equation of this tangent line can be written in the form y=mx+b 2.For the equation given below, evaluate y^1 at the point(1,-1) . (6x-y)^4+2y^3=2399. 3.Find the...

Homework Statement Find the slope of the tangent line to x tan y = y - 1 when y = pi/4 Homework Equations The Attempt at a Solution I can't seem to get the derivative. Here's what I do. First I used the product rule the left side of the equation and got sec^2 x dy/dx + tan...

Homework Statement Find d^2y/dx^2 in terms of x and y. x^2y^2-2x=3 Homework Equations property rule, chain rule, quotient rule, The Attempt at a Solution I can do this the long way, but there must be a shorter solution. Can I simplify it? I've found dy/dx=(-xy^2 +2x)/(2x^2y)...

Determine (dy/dx) using implicit differentiation. cos(X^2Y^2) = x I'm really confused what to do now..i think the next steps are: d/dx [cos(X^2*Y^2)] = d/dx [x] = -sin(X^2*Y^2)* ((X^2*2Y dy/dx) + (Y^2*2X)) = 1 = -2YX^2 sin(X^2*Y^2) dy/dx + -2XY^2sin(X^2*Y^2) = 1 = -2YX^2 sin(X^2*Y^2)...

I looked through my notes and couldn't figure out how to differentiate (x - y) using implicit differentiation. Could someone help with that and I should be able to work out the rest of my question :)

Question: Find dy/dx by implicit differentiation 4x^2 + 3xy - y^2 = 6 Attempt: Ok, just a forewarning that I suck at differentiations, limits, what-not, so.. Following my textbook, it says I should Differentiate both sides of the equation So... (d/dx)(4x^2 + 3xy - y^2) = (d/dx)(6)...

Homework Statement x^{}2(x-y)^{}2=x^{}2-y^{}2 Homework Equations The Attempt at a Solution I can get this far: x[2(x-y)(1-dy/dx)]+2x(x-y)=2x-2ydy/dx Any small hint as to where to go from here would be much appreciated.

Hello there! Please help me relieve my confusion. Thanks! For \frac{d}{dx}[y^{3}] , why do you need to use the chain rule on this equation? Basically, the chain rule is used on almost every function right? It is just that we do not see the dx/dx since it equals one, for example...

Homework Statement Hi everyone, name is Ryan. This is my first post here, seems like a very beneficial forum. I look forward to being helped and helping others. Anyway I'm trying to teach myself Implicit Differentiation but there doesn't seem like much useful resources online and I don't quite...

Hi guys, I have a question on an implicit differentiation problem. I get two different answers depending on how I do it and the answers are different (not just looking, but different). The problem is [tex] \frac{x+3}{y}-4x-y^2=0 [\tex]. One option is to just differentiate as it stands and you...

Homework Statement I just got started on this, and am not grasping the WHOLE idea. 1.xy=25 The answer says -y/x 2.x^2+3xy+y^2=15 And this says -y^2/x^2 Homework Equations 1. dy/dx(xy)= dy/dx(25) 1=0 ? 2.dy/dx x^2+3xy+y^2= dy/dx 15 2x+3+y(dy/dx) =0 The...

Homework Statement Find dy/dx by implicit differentiation when it is known that y^2 + xsiny = 4 Homework Equations The Attempt at a Solution 2y dy/dt + xcosy dy/dt + siny = 0 2y dy/dt + xcosy dy/dt = -siny dy/dt + dy/dt = -siny/2y/xcosy I'm sure I'm doing it wrong so I...

assistance asap is needed ! Using implicit differentiation, find dy/dx given that: cos(xy^2) - (x^3+y) / (x+1) = sec(x)sin(y) i am horrid at these, i came up with a few lines, please check them -sin(xy^2)[(y)^2+(2y)(dy/dx)(x)] - [ {(3x^2)(x+1)-(x^3+y)} / (x+1)^2] = sec(x)tan(x)sin(y) +...

In a problem where I need to use implicit diff. to find the slope of a line such as: y^2 + x^2 = 9 2y (dy/dx) + 2x = 0 dy/dx = -y/x Where does the (dy/dx) after the 2y (in the second part) come from? I've already differentiated y^2, x^2, and 9. Why isn't it just 2y +...

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...

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

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

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...

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...

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...