id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ajrhss-2636	Abdukakhhorov Izzatillo Shavkatali ogli	THE DERIVATIVE OF SOME FUNCTIONS BY DEFINITION	2025	4	.pdf	application/pdf	1689	51	74	→ +  − = =  ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )2 0 2 0 2 0 2 0 1 0 1 0 1 0 1 0 0 0 lim lim x x x x x x x x x x x x x x x x         +  →  → +  − +  +  Thus, based on equations (2) and (3) above, we write the state of; ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )0 0 0 0 2 0 3 0 4 0 5 0 0 1 0 2 0 3 0 4 0' x x x xn n n n x x x x ny x x x x x               =    ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )0 1 0 0 0 2 0 1 0 1 0 1 0 ' ln ln 1 xn n nx x n n n n x x x x x        − − − −     +     ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )1 0 2 0 0 1 0 2 0 1 0 3 0 1 0 2 0 ' ' ln ln ln ln n n n n n n n x x x x x x x x x          − − − − − −  + +  ( ) ( ) ( ) ( )3 0 1 0 4 0 3 0 ' ln ln n n n x x x x     − − −  + +  American Journal of Research in Humanities and Social Sciences Volume 32 January-	cache/ajrhss-2636.pdf	txt/ajrhss-2636.txt