AP Calculus, last minute reviews

Here is a link to a group of questions and answers to volumes, obtained by rotating graphs around a given line.
http://hotmath.com/help/bookindexes2/minicalcgt/problems_6_1_1.html

Below is a set of practices for derivatives and Tanget lines
http://hotmath.com/help/bookindexes2/minicalcgt/problems_3_1_1.html

jason said...

How do you find the derivitive of a funtion that has more than one unknown variable?

Respond:

Excellent question!

Find dy/dx using implicit differentiation.

Hint

Start by using the Product Rule on the two terms on the left.

Step 1

We take the derivative of both sides to obtain

(x²) ′y + x²y′ + x′y² + x(y²) ′ = (3x) ′ .

Then, we simplify to

2xy + x²y′ + y² + x2yy′ = 3

2xy + x²y′ + y² + 2xyy′ = 3.

Hint

Solve for y′ by placing all y′ terms on one side.

Step 2

Rearranging so that all terms containing y′ are on one side, we have

x²y′ + 2xyy′ = 3 – 2xy – y²

y′ (x² + 2xy) = 3 – 2xy – y²

Hint

Solve for y′ .

Step 3

Solve for y′ .

You can factor out x from the bottom if you like, but it doesn't really simplify the answer.

Also, go here for thje list aof all the general Calculus formulas you need to know.

http://www.calculus-help.com/funstuff/cheatsheet.html

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