ßQ4. Egon Eichwald und Andor Fodor. 



tg(^_,^^ tgx-tg>_ 



^^ •' 1 + tgx.tgy 



2tgx 



tg2x= — . 



^ I — tg2x 



Differentialrechnung. 



Ableitungen. 



dx°_ ^_, d_ J____I_ ± }___ J_ A|~-J_ JL 

 dT~°-^" •dxx" x-^" dxx" ^ °x- + i- dx'^~ 2 "[/^ 



d ° 1 ° . d ,"— m 1", 



— x=: — . x^-i; — X" = — . 'x'"-". 



dx' n ' dx' n ' 



da^ , de^ 



— — =a^lna: -^ — =e^. 

 dx dx 



® 1 . dlnx 1 



dx l+x2 



^ = 0: ;^a.ffx)r=af(x). 

 dx dx 



^ [f ( X ) ± g ( X )] = f ' (X ! ± g' (X). 



^f(x).g(x) = f(x).g(x) + g'(x).f(x). 



d 1' (x) _ g (. X j f ' (XI — f (X ) ■ g' (x) 

 dx^" [grx)]2 



Einführung neuer Variablen. 



y = f(u), wo u = g(x;): y = f(u), u = g(v), v = li(x); 

 dy_dy du dy _ dy du dv 

 dx""du'dx" dx "~ du'dv' dx' 



dlnf (x) _ f^xj 

 dx ~f(xj* 



