hey, trying to do a question, but don't know how to differentiate factorials, how would u differentiate (x-2)! any help would be great thanks
You would need to use the gamma function
$\displaystyle \Gamma(x)=\int_{0}^{\infty}t^{x-1}e^{-t}dt=(x-1)!$
$\displaystyle \Gamma(2x-1)=\int_{0}^{\infty}t^{2x-2}e^{-t}dt=(2x-2)!$
Why do you need to take the derivative of a factorial?
From here you could take the derivative of an integral I guess.
I hope this helps.
im trying to find the derivative of cos x using the series
$\displaystyle cos x = 1 - (x^2/2!) + (x^4/4!) - (x^6/6!)$
i worked out that each term could be given by
$\displaystyle Tn = n^(2n-2)/(2n-2) * (-1)^(n+1) $
although now that i think about it, thats not going to help is it.
would it be possible just to differentiate each term ie $\displaystyle (x^2/2!)$ becomes $\displaystyle x $ and repeat for each term, how would u state that you are assuming something is continuing though.
Two things...the derivative of cos(x) is -sin(x) and secondly that is the series $\displaystyle cos(x)=\sum_{n=0}^{\infty}\frac{(-1)^{n}x^{2n}}{(2n)!}$ is exactly the series you are talking about?
Dont believe me put in values for n,1,2,3,4 and you will get the same series that you listed above