10

This week we learned related rates and angle of elevation along with the implicit first and second derivatives. Implicit derivatives isn't too bad, i wasn't there for the notes but i still understand what i'm doing.

RELATED RATES: the problem can be given as a picture or they can tell you certain things which require you to draw the picture out yourself. Equations are sometimes provided and remember that you can only have one variable that you don't know what it is.

1. Identify all of the variables and equations.
2. Identify what you want to find.
3. Sketch and label.
4. Write an equations involving your variables.
5. Take the derivative with in terms of time.
6. Substitute the derivative in and solve.

IMPLICIT DERIVATIVES

1. take the derivative of both sides
2. everytime you take the derivative of y note it with dy/dx or y^1
3. solve for dy/dx


EXAMPLE: y^6+y^4-10y-x^4=-8
6y^5dy/dx+4y^3dy/dx-10dy/dx-4x^3+0
dy/dx(6y^5+4y^3-10)=4x^3
dy/dx=4x^3/6y^5+4y^3-10

once again, i get the whole derivatives concept, however, i have no idea what i'm doing with related rates. i can draw the picture, but thats about it. i have a hard time applying outside things or relating thing that aren't given to the problem. any help would be great, thankssssssss.

post # 10

okay, i have like no notes from all week because i was not at school, but i learned some stuff anyway. So at the beginning of the week, the class learned how to take the second implicit derivative.

okay, so as i mentioned in my last post, implicit derivatives have both an x and y variable, and when you take the derivative of y, you note it with dy/dx or with a y'. After you do that, obviously you solve for dy/dx or y'.

alright, so when you take the second derivative, you do the same thing, except when you take the derivative of dy/dx, it becomes d^2y/dx^2

after that you simplify and solve for d^2y/dx^2. and that is all.

ok, first here is an example of a normal implicit derivative: y^3+y^2-5y-x^2=-4
First you just take the derivative, but don't forget to note the derivatives of the y's! So you get: 3y^2(dy/dx)+2y(dy/dx)-5(dy/dx)-2x=0

Then you have to solve for dy'dx, so you get:
dy/dx(3y^2+2y-5)=2x which then is further solved for to get dy/dx=2x/(3y^2+2y-5)

Now, for the second derivative, you just change the dy/dx into d^2y/dx^2 and take the derivative of the right side of the equation again.

i'm pretty sure that's how it is worked, but then again, i wasn't in class when we learned it.

now, i guess the thing i do not understand anything we learned after the second derivative, and that is really only because i have been absent and have not copied the notes yet and have not tried to learn it.

-mher

WEEK TEN

We learned a lot this week.

On Monday we learned how to find the second derivative (d^2y/dx^2) of implicit derivatives. The only difference between this and regular implicit derivatives is that you first of all take the second derivative and where dy/dx ends up in the second: plug in what you got for the first.

On Tuesday we learned about Related Rates.
Steps for finding the Related Rate:
Identify all variable and equations.
Identify what you are looking for.
Make a sketch and label.
Write an equation involving your variables. Know that you can only have one unknown variable, so a secondary equation may be given.
Take the derivative with respect to time. aka: (dy/dt) or (dx/dt).
Substitute in derivative and solve for the rate.

We also worked a problem that Ms. Robinson said would be on the AP exam, so make sure you make note of it. It was the concentric circles in the pond example.

On Friday we did a problem on Angle of Elevation that I did not understand.
It was: Find the rate of change of the angle of elevation of the camera in the figure 10 seconds after life off. If the rocket is rising according to the position equation y=50t^2.
I also do not understand any of the word problems relating to the Related Rates. Can someone maybe explain this to me?
　

post 10

26Another week down in calculus and we kept with implicit derivatives and started with related rates and finding the angle of elevation. All of these were easy for the most part. The most complicated has to be finding the angle of elevation. The steps for related rates are:
1. Pick out and identify all variables and equations
2. Figure out what you are looking for
3. Make a sketch and label
4. Create an equations including all of the variables
5. Take the derivative of the equation with respect to time
6. Substitute into derivative and solve for what ever you are looking for
66Related rates are not complicated untill you start finding the angle of elevation using related rates.

28Implicit derivatives are also not complicated at all. It is pretty much the same as taking a regular derivative with some small twists. The steps for this is:
1. Take the derivative of both sides like you would normally take a derivative
2. Note when you take the derivative of y by using dy/dx or y
3. Then just solve for dy/dx as you were solving for x

For what I am having problems with, I am not having the greatest success with completing every problem having to do with find the angle of elevation when using related rates to find it. But I do not have much problem at all just finding the related rates by itself. I sometimes just lose track of what I am working with. If anyone has any ways that may help me with keeping track of everything I am working with it would be appreciated.

Posting...#10

Calc was kind of hard for me this week we did implicit derivatives first ones and seconds ones…O.o and we also did Related rates implicit derivatives wasn’t really that hard but I have trouble with related rates in a few ways. I know the steps which are
1. Identify all variables and equations
2. Identify what you are looking for
3. Make a sketch and label
4. Write an equation involving your variables
5. Take the derivative with respect to time
6. Substitute in derivative and solve.
Now I know the steps of related rates but my biggest and I mean a big problem for me this is a problem for me in optimization too and that is step four. For related rates I don’t know how to find an equation or what equation to use for an example of a circle if you’re looking for area the equation would be: A= (pie)r^2 which I wouldn’t of know but should of and for optimization I still can’t find a primary and secondary I have to say this is my biggest problem in calculus.

Like for area and volume if you have a problem like 20(in our packet)
20. volume all edges of a cube are expanding at a rate of 3 centimeters per second. How fast is the volume changing when each edge is (a) 1 centimeter and (b) 10 centimeters?
I know how to draw the picture and tell my variables and what im looking for its just when I get to step 4 and have to make and equation.

# 10 !

This week in calculus wasn't too hard. We learned first and second implicit derivatives. Also we learned related rates and angle of elevations. We also took a test on Tuesday on first and second implicit derivatives, at least I think it was tuesday. anyways, related rates are a breeze. they are kind of like optimzation, but not as difficult. i have no problem with those: here are the steps.

1. identify all the variables/equations
2. identify what you are looking for
3. make a sketch and label (extra points!)
4. write out the equation
5. take derivative of both sides (remember to put dy/dt and dx/dt behind your derivatives)
6. plug in all variables given

also, implicit derivatives are very easy.

1. make sure the problem has x & y values
2. take the derivative of both sides *noting the y-values with dy/dx*
3. solve for dy/dx.

and to solve for dy^2/d^2x, you just take the derivative of your first derivative.
also, angle of elevations. to tell you the truth, i forgot to bring my notebook home this weekend, so i don't really know how to explain it. we just learned it on friday, and it kinda went out of my memory. it was kind of like related rates, but more difficult. i didn't really catch on to them as good as i did with related rates, im not sure why. hopefully it will get easier, if anyone has a general idea of what an angle of elevation is, can you please help?

post 10

the tenth week of calculus has been exactly like the first nine. we learned implicit derivatives. and we learnedd the first and second implicit der tests.
First derivative

1) take the derivative
2) everytime you take the derivative of y you note it by saying that it is y prime. You do this by putting one of two things. You can either put dy/dx or y^1.
3) Once you finish the derivative you then solve the equation for dy/dx of y prime. You do this by using simple algebra.

Second Derivative

1) first you find the first derivative and solve it for dy/dx by using the steps for the first derivative steps.
2) you then take the second derivative of the solved equation. Plugging in d^2y/d^2x everytime you take the derivative of y again. and where you have dy/dx you plug in your solved equation for that.
3) once you have everything plugged in and ready to go you then solve for d^2y/d^2x
This is also done by using simple algebriac methods.

im still not too goood at optimization becuase i always cant find the primary and secondary equations and i never know what to do w/ the missing variables even though i know how to optimize things haha

post # ten

This week in calc i learned two things, first and second implicit derivatives. These concepts are pretty basic to calc. they involve taking a derivative and solving an equation.

First derivative

1) take the derivative
2) everytime you take the derivative of y you note it by saying that it is y prime. You do this by putting one of two things. You can either put dy/dx or y^1.
3) Once you finish the derivative you then solve the equation for dy/dx of y prime. You do this by using simple algebriac skills.

Second Derivative

1) first you find the first derivative and solve it for dy/dx by using the steps for the first derivative steps.
2) you then take the second derivative of the solved equation. Plugging in d^2y/d^2x everytime you take the derivative of y again. and where you have dy/dx you plug in your solved equation for that.
3) once you have everything plugged in and ready to go you then solve for d^2y/d^2x
This is also done by using simple algebriac methods.

One thing that I still dont understand unfortunatly is taking the derivative of a graph. Like when they give you graph and say take the derivative. lol it messes with me like i know how to do i just cant apply it i always get it wrong...i need more help with this.

Post #10

This week was all about first and second implict derivatives and related rates. I'm actually comfortable with doing implict derivatives. The only problem I have sometimes is forgetting to put dy/dx or little mistakes with algebra. Related rates, however, I'm having difficulty with. It kind of reminds me of optimization, which I'm really really really bad at. Some of the problems that are straight forward, I can sort of do, but the others are just too complicated.

so implict derivatives:

Steps
1. take the derivative of both sides
2. everytime you take the derivative of y note it with dy/dx or y^1
3. solve for dy/dx

Example
y=sinxy
dy/dx= cosxy(x(dy/dx)+y)
dy/dx-xcosxy(dy/dx)=ycosxy
dy/dx= ycos(xy)/1-xcox(xy)


now second derivative of impliit derivatives:
It is the same steps except when you take the derivative of dy/dx, it becomes d^2y/dx^2.

Example
x^2+y^2=25 Find d^2y/dx^2
2x+2y(dy/dx)=0
dy/dx= -x/y
d^2y/dx^2= y(1)-[x(dy/dx)]/y^2
d^2y/dx^2= -y-x(-x/y)/y^2
=((y^2/y)+(x^2/y))/y^2
d^2y/dx^2= (-y^2+x^2)/y^3


Ralated Rates are waht I'm really having trouble with. Finding the equations is what trips me up. Does anyone have any advice on how to attack these problems? haha

Number 10

This week in Calculus was not that hard..we learned first and second implicit derivatives and then we learned some other stuff that I don't understand. I'm not even sure what its called, but I do not understand the stuff with drawing a shape then doing all the nonsense after..the new way of optimizing maybe?

But anyways, let me explain what I know how to do..
which is taking the second implicit derivative :)

You know when something is an implicit derivative when it has two variables, a x and y. Also, these types of problems have an equal sign. YOU MUST TAKE THE DERIVATIVE OF BOTH SIDES.

So, first you take the derivative of both sides like usual, but the new thing is, EVERY TIME you take the derivative of y, you must mark behind it dy/dx. This is for later reference that you took the derivative of y and not x.

Then you simplify it in terms of dy/dx.

After, if taking the second derivative, you take the derivative again and if you take a derivative of dy/dx, it becomes d^2y/dx^2.

Then you must simplify and plug in your dy/dx you got previously.

So, lets work an example problem!

xy = 4
(x)(dy/dx)+(y)(1) = 0 [TAKE DERIVATIVE OF BOTH SIDES]
x(dy/dx)=-y [START SIMPLIFYING FOR DY/DX]
dy/dx = -y/x [SOLVE FOR DY/DX]

Now, take the second derivative...

d^2y/dx^2 = [ (x)(-dy/dx) - (-y)(1) ] / x^2
Now plug in your dy/dx and simplify.

The thing I really don’t understand is the stuff we learned after this. When you are given a word problem and you have to just figure everything out..I’m having trouble figuring out what everything is and how you solve for whatever your looking for.

Post Number Ten

This week i felt i caught on okay in class, but when i try to do problems by myself i feel like i don't know what to do and where to even start. Story of my life though right?

Well this week we learned related rates and angle of elevation. I understood related rates at first, but now i'm not so sure of myself. But here's the steps for related rates:

1. Identify all variables and equations.
2. Identify what you are looking for.
3. Make a sketch and label.
4. Write an equations involving your variables.
*You can only have one unknown so a secondary equation may be given
5. Take the derivative with respect to time.
6. Substitute in derivative and solve.

The problems can be given to you in two ways. You can either be given the equation and such or you may need to find them. I personally do better at when there given, but that's expected.

Ex:

The variables x and y are differentiable functions of t and are related by the equation y = 2x^3 - x + 4. When x = 2, dx/dt = -1. Find dy/dt when x = 2.

Since everything is given you can skip straight to the derivative.
dy/dt=6x^2dx/dt - dx/dt
Now plug in all your givens in order to find dy/dt.
dy/dt=6(2)^2(-1) - (-1)
dy/dt= -23
That was fairly easy and i can do all problems like that, but whenever the equation is not given i struggle with that. I guess it's because i sucked at optimization too and recognizing what equations to use when. Hopefully i'll get the hang of it.

Now for angles of elevation I can't really explain because I didn't really catch on to that in class when being taught. I'm not good at imagining a sketch to draw in the first place so if anyone can help me with that it'd be greatly appreciated. I need all the help i can get in everything so if anyone's up for that that'd be great :)

Post 10

So this past week and the Friday before that we started the second nine weeks. The first thing we learned was implicit derivatives.

Implicit derivatives are just like regular derivatives, except they involve x and y, and when you take the derivative of y, you must always note it with dy/dx or y'. After dy/dx is noted, you need to solve for dy/dx, giving you your implicit derivative.

The second thing we learned was second implicit derivatives. They are just like taking the second derivative of a normal function, except just like implicit derivatives, it involves x and y. When taking a second implicit derivative, you just take the derivative of a first implicit derivative. You note a second derivative as d^2y/dx^2. Just like in a first implicit derivative, you always need to note whenever you take the derivative of y, only in the second derivative, you're finding the second derivative, so you plug your first derivative in anywhere dy/dx is noted.

The third thing we learned this week was related rates. The steps for related rates are as follows:

1. Identify all variables and equations

2. Identify what you are looking for

3. make a sketch and label

4. Write an equation involving your variables

5. take the derivative with respect to time (dn/dt)

6. subsittute in derivative and solve.

Finally, this week we learned how to find angles of elevation. This has to be the part where I am struggling the most in. I was just trying to do my homework and I couldn't really do most of it. I did number 43 fully because it was just like one of the examples we did in class, but I got confused on the rest.

For number 44, I'm confused about what x is supposed to be or if we're supposed to find x? Also, I'm not sure if x is supposed to be 25, because where the problem says there is 25 feet of line out. It dosen't really say if the fish is right on top of the water and that is where the line ends or if there is line beneath the water? Even if I did have this information, I'm still really confused on what to do next. The same goes for numbers 45 and 54.

Post.

Before I start word counting, let me just say that I am never missing another day of school. Ever. I was sick for like a week, and when I finally decide to go to the doctor to get well (which, might I add, cortisone shots are amazing..for about the first 9 hours), I come to school and am bombarded with all kinds of things. Homework. Quiz. And the Like. Majorly upset about that one.

So calculus. Yeah.

I was fine up until angles of elevation (day I got back, and was just completely out of my mind loco to say the least, the very least). I got implicit derivatives, and since I've been doing Calculus homework all weekend, I get/somewhatlove related rates. In an effort to gain wordage-word?-I shall complete a Calculus problem (wonderful right??).

Implicit derivatives.

As in my last post, I believe the trick to implicit derivatives is just remembering to put y' or dy/dx when taking the derivative of y. Simple as that. An application of related rates...:

You have to identify what you are looking for and what you are given. Not only does this make it easier on you, it's kind of necessary, especially when you want those points on free response questions (or so I'm told). You also have to realize that when you are doing related rates, you have to put dy/dt or dx/dt or whatever whenever you are taking the derivative of some variable in relation to time (hence the t). So given that:

Given xy = 4

you want to know what dy/dt equals given x = 8 and dx/dt=10.

Take the derivative (product rule):

dx/dt y + dy/dt x = 0
Plug in everything:

dy/dt = -10y/8

= -5y/4

So, that's related rates.

For what I do not know:

1. Would anyone like to explain the steps(?) for angles of elevation?
2. Also, what exactly did everyone do on Wednesday?
3. On the homework that she gave us, does anyone get number 54? the shadow one? kind of lost!?

There is probably about a hundred more questions, but I'm going to go and finish the massive amount of work I have from missing one, yes ONE, day of school...Sorry.