# Calculus

Discussion in 'General Math' started by null, Nov 3, 2003.

1. ### nullGuest

In my AP calc class, my teacher told me to find the f'(x), then f''(x), then
f'''(x), and so on. I would know how to do f'(x), but after that, I'm
mysted.

with all the axn(n-1)(n-1)(n-1)^(n-n), whatever, he told me the answer to
that would be (e.g.) 5!

Now I never heard of a number with a ! symbol after it. Can anyone explain

null, Nov 3, 2003

2. ### William SpringerGuest

Ok, you know how to find f'(x). Now take the derivitive of that, and
you'll have f''(x). Take the derivitive of THAT, and you'll have
f'''(x). And so on..

n! is n factorial, which means n * (n-1) * (n-2) ... * 3 * 2 * 1, with
0! defined to be 1. So 0!=1, 1!=1, 2!=2, 3!=6, 4!=24, etc.

William Springer, Nov 3, 2003

3. ### Nat SilverGuest

If y = x^5, then y' = 5x^4, y'' = 5*4x^3, y''' = 5*4*3x^2,
y'''' = 5*4*3*2*x and y'''''= 5*4*3*2*1 = 5! (by definition of factorial).

See the reference below:

http://mathworld.wolfram.com/Factorial.html

Nat Silver, Nov 3, 2003
4. ### Thomas OstergardGuest

That is the factorial symbol. It means you multiply by all the integers
below it, ex.

5!=5x4x3x2x1=120
6!=6x5x4x3x2x1=6x5!=720

Hope this helps.

Thomas

Thomas Ostergard, Nov 15, 2003