2006-07-07 07:35:43 · 9 answers · asked by laurewen_of_mirkwood 1 in Science & Mathematics ➔ Mathematics
With the usual definition of x! as a product, it is only defined for integers and so is not a candidate to be differentiated. There is a way to extend the definition of x! to non-integer values, and that relats to a function called the Gamma function. The Gamma function can be differentiated, but given that you are doing calculus, you don't yet have the background.
If you allow me to guess, you are probably wanting to take the derivative because you want to use L'Hopital's rule on a limit. This tends to come up when studying series, in which case, you should use the ratio test rather than a limit test of some sort.
2006-07-07 08:43:13 · answer #1 · answered by mathematician 7 · 2⤊ 0⤋
Factorial is defined for integers only, hence the derivative cannot be defined. However the Gamma function extends the factorial to real and even complex numbers:
Gamma(z+1) = z!
and could be differentiated.
2006-07-07 08:28:34 · answer #2 · answered by ExwiseGuy 1 · 0⤊ 0⤋
The definition of the factorial x! applies only for positive integral values of x. A plot of x! vs. x is a bar graph. That function does not have derivatives. (It's not continuous.)
Hope that helps!
2006-07-07 07:40:12 · answer #3 · answered by Jay H 5 · 0⤊ 0⤋
x!' = x! * int(0, oo)[e^(-(x + 1)t)/(1 - e^-t) dt]
But I agree with the other mathematician that this is probably not what you're looking for and you probably weren't asked this directly.
2006-07-08 07:52:36 · answer #4 · answered by mathematician 2 · 0⤊ 0⤋
y=x!
y=x*(x-1)*(x-2)*.....+(x-(x-1))
ln(y)=ln(x*(x-1)*(x-2)*.....+1)
ln(y)=ln(x)+ln(x-1)+ln(x-2)+......+ln(1)
y'/y=1/x+1/(x-1)+1/(x-2)+......+0
y'=[1/x+1/(x-1)+1/(x-2)+......+0]*x!
Of course, I'm just playing around here, but there's a dirty answer for you. Completely useless function, undefined at every whole number!
2006-07-08 00:41:01 · answer #5 · answered by Anonymous · 0⤊ 0⤋
Jay H is correct.
2006-07-07 07:42:04 · answer #6 · answered by binaryFusion 5 · 0⤊ 0⤋
dx / dx = 1
The answer is 1
2006-07-07 07:58:33 · answer #7 · answered by envi v 2 · 0⤊ 0⤋
artwork from the outdoors in utilising the chain rule a pair circumstances. y` = (a million / cos(lnx)) * d/dx [cos(lnx)] = (a million / cos(lnx)) * (-sin(lnx)) * d/dx [lnx] = (a million / cos(lnx)) * (-sin(lnx)) * (a million/x) = -(sin(lnx) / xcos(lnx)) = -tan(lnx) / x
2016-11-01 09:30:37 · answer #8 · answered by ? 4 · 0⤊ 0⤋
i dunno.
2006-07-07 07:38:40 · answer #9 · answered by the redcuber 6 · 0⤊ 0⤋