Can anyone help me with my AB Calc?

Sure, but I don't think it would be time productive to type out the entire theory of calculus. What chapter are you on and what don't you understand.

oh haha other post, for implicit differentiation:

-Use d/dx as a function over your entire equation
-Factor out the dy/dx and solve for it
-You can use the d/dx for almost any equation for any term
-break up the equation over addition and take the derivate of each single term

Example: x^2 + y^2 = 49
now, you are allowed to do almost anything provided you do it to both sides correct.
You can add one to both sides
You can take the square root of both sides
You can cube both sides
Right?
You can also take the derivate of both sides
d/dx(x^2 + y^2) = d/dx(49)
d/dx can be split over addition, right?
d/dx x^2 + d/dx y^2 = d/dx 49
When you do this, I recommend you always use the chain rule. So here it goes...
2x dx/dx + 2y dy/dx = 0
so dx/dx cancels out
2x + 2y dy/dx = 0
You want to isolate and solve for dy/dx
2y dy/dx = -2x
dy/dx = -x/y
Does that help.
The best way to understand I think is to treat d/dx as a function, that you are allowed to do to both sides of the equation and it will still be equal. All d/dx does is find the change of some variable in relation to x. dy/dx is how much y changes with x. And since slope is defined as delta y/delta x, taking the derivative(d/dx) will give you the slope. I hope this helps. I can give another example if you want, or answer any specific questions.

I did my work on paper, but I cannot format the picture to fit right now, so I'll walk you through it. This type of problem is called a related rates problem.
The first step is to write down all of your known values as well as your unknown ones. I'm going to let K stand for Theta for the angle.

dx= 0 ft/s
dy= 8 ft/s
y= 25 ft
x= 60 ft
K= ?
dK= ?

Next draw a picture and label all of your values.
This should basically be a right triangle with the right angle in the bottom right hand corner and the longer leg on the bottom

Now let your x be the horizontal line and your y be your vertical line and put in the values that you know. O will the the bottom angle on the left.

Now write the equations that you know that have the variables that you have in them. If there are any other variables, then this will not work.

For this problem use the definition for tangent:

tanK= y/x

Since you know y and x, use inverse tangent to find theta (it should be 22.62 degrees). Now you need dK. To find that take the derivative of the above equation. You should get this:

xdy - ydx = (secK)^2dK
x^2

Now solve the equation for dK and plug in your values. The final equation should be:

dy(cosK)^2 = dK
x

And your final answer should be 0.11 degrees per second.

I hope that you understood that!

If anyone sees a problem with this, please tell me. But this should be right.

Advice for the future: if you are ever stuck on a calculus problem that can be graphed or drawn, do so and see if it makes any more sense than it did before. The same thing applies for Physics...probably not a good thing for chronic doodlers though. Good Luck! :D

That's a good solution, I didn't check to see if the math is right. If you can't do a problem, before you ask anybody else, write an equation in terms of what you are trying to find. Any equation. For this problem it would be tan(k) = y/60. Setting up and solving the problem is usually the hardest part. Once you get an equation, fill in as many values as you can, then see if it is able to be solved. Once you're there, if your stumped come here, but that is usually the hardest part of the problem, you just need to figure out how to set it up

chessmaster1990 wrote:That's a good solution

Thank you :D

Hey guys, I'm new to course-notes forum, but not new to calc. I took AB Calc last year and I got a 5. Here's a neat website for AB, BC Calculus and Physics.
It has great tutorials.
http://www.archive.org/details/ap_courses
Hope it'll help. Although, dont think ull get a 5 with just that website. U shud do all ure hw from ure book and if u want to get a 5, U should buy a barrons review book.