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Thursday, March 23, 2006

Derivatives of, and Definitions of a derivative

So, I'll start my scribe now, since it involves no pictures, it should be quick n' easy. Woohoo! Anyways, here I go, Enjoy!

I came late to Calculus (oh no!) by 15 minutes (a big oh no!), so I missed the quiz. Alarm didn't go off, mom did. Boy that wasn't fun. Anywho, we wrote in our math dictionaries. The notes looked like this:

Derivative of:

A constant function

f(x) = k f'(x) = lim f(x+h) - f(x)
h->0 h

The Derivative of a = lim k-h
constant funcion h->0 h
is ZERO.
= lim 0
h->0 h

= 0

A linear function

f(x) = mx+b f'(x) = lim f(x+h) - f(x)
h->0 h

The limit of a = lim [m(x+h)+h] - [mx+b]
linear function h->0 h
is the slope of
the line. = lim mx + mh + b - mx - b

= lim mh
h->0 h

= lim m = m

So, after all those notes, Mr.K said, we are to do something different, but are going to go back to that stuff up there in future classes. He needs to pay attention to these things first he says. So, different notes, but related, are appearing on the board.

The Definition Of A Derivative

f'(x) = lim f(x+h) - f(x)
h->0 h

A derivative is:

The slope of a tangent line
A rate of change

A summary of derivative rules.

Constant function : f(x) = k f'(x) = 0
Power function : f(x) = x^n f'(x) = nx^(n-1)
Constant times a function : f(x) = kg(x) f'(x) = kg'(x)
A sum or difference of a function(s) : f(x) = g(x) +/- h(x) f'(x) = g'(x) +/- h'(x)

*note the +/- is the + over the - , so we're not dividing here. I couldn't find that character on the character map. Sorry for the incovinience.

Ex. Find the derivative of :

f(x) = 3x² - 2x + √x - 5
f'(x) = 3▪2x - 2 + (1/2)^x^-1/2
= 6x - 2 + 1/2√x

*note the √ is square root, and the ^'s are to the power of. Since I've never done a proper scribe, tell me all those commands that give it the oh so nice look.

I hope this helps. Next scribe will be Temesgen.

But now, there's only 2 of us, Calvin dropped, so, we have to work something out. Scribing once a week is a lot of work!


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Blogger Lani said...

Hi Van,

I really enjoy reading your scribes; your personality comes right through! I can picture Mom right now ☺

And I appreciate your desire for excellence in your scribe's appearance. I'm sure there must be many ways to work with symbols; I'm no expert in this area. Would this help if you are on a machine with windows xp?

Use the Character Map. To open Character Map, click Start, point to Programs, point to Accessories, point to System Tools, and then click Character Map. For information about using Character Map, click Help in Character Map.

I can tell you've taken lots of effort with these last two scribes and know it must have taken time. Are you finding that once you've explained it to us all, that it's clearer for you too? If that's so, is that a reason to accept the challenge of one scribe a week as an opportunity to excel?


25/3/06 08:55  

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