calculate-d-x-dx-

Question Number 42514 by jbm last updated on 27/Aug/18

c a l c u l a t e d (x!) / d x = ?

Answered by tanmay.chaudhury50@gmail.com last updated on 27/Aug/18

y = x!

y = x (x - 1) (x - 2) (x - 3) \dots 1

l n y = l n x + l n (x - 1) + l n (x - 2) + \dots + 1

\frac{1}{y} \frac{d y}{d x} = \frac{1}{x} + \frac{1}{x - 1} + \frac{1}{x - 2} + \dots

\frac{d y}{d x} = x! (\frac{1}{x} + \frac{1}{x - 1} + \frac{1}{x - 2} + \dots)