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# AP Calculus AB

An interactive log for students and parents in my AP Calculus class. This ongoing dialogue is as rich as YOU make it. Visit often and post your comments freely.

## Monday, November 14, 2005

### Bank of Derivatives (so far...)

Our rules SO FAR...

Any constant: d/dx C = 0

Power Rule: d/dx cx^n = ncx^(n-1)

Product Rule: d/dx f(x)g(x) = f(x)gÂ(x) + fÂ(x)g(x)

Quotient Rule: *lo di hi minus hi di lo all over lo lo*
In mathematical termsÂ.
d/dx f(x) / g(x) = [ g(x)fÂ(x) - f(x)gÂ(x) ] / [ g(x) ] ^2

There were also the derivatives of the six trig functions that Mr. K proved in the end of class today.

d/dx sin x = cos x--------------- d/dx csc x = - csc x cot x

d/dx cos x = -sin x-------------- d/dx sec x = sec x tan x

d/dx tan x = sec^2 x----------- d/dx cot x = - csc^2 x

See any patterns?
Look at the functions that starts with ÂCÂ, their derivatives are all negative.
The function tan x and cot x, their derivatives are squared.

So today we started off our class with a problem. Boys vs. Girls. Who won the race between Willy the wallaby and Roo the kangaroo?

A verytrickyy tricky question. Yet very funny in some sense. We need more practice on it. And we shall get another one tomorrow =)

For the rest of the class, we filled out our bank of derivatives with a couple of new ones. ItÂs growing larger everyday (except weekends).

That was pretty much what we did today. I have three words before I who's you whos the next scribe and that is...

MEMORIZE MEMORIZE MEMORIZE!

Next Scribe is Prince. Sorry Prince. Hope you're feeling better by tomorrow. I think your the last one. =S I'm not sure.

• At 9:31 PM CST,  Mr. Kuropatwa said…

An absolutely stunning scribe post Sarah!

I most liked the reflection you did on looking for patterns. As I've said before: "Mathematics is the science of PATTERNS!" It's always a good idea to try to identify the patterns in new things that we learn. It also helps to try to find any similarities with things we've learned earlier.

Keep up the good work!

• At 9:24 AM CST,  steve said…

Nice post Sarah, the rules really stand out when in colour. Good job.