ß04 Egon Eichwald und Andor Fodor. 



tgx — tgy 



tg(x— y) 

 tg2x 



1+tgx.tgy" 



2tgx 

 1 — tg2 x" 



Differentialrechnung. 



Ableitungen. 



dx "^•^" ' dx* x ~ x2' dx'x" ~ "x° + i' dx'^~ 2 ' \/7' 



dn < n 1 11 n 

 ,- 1 , : d ,, — ra ,, 



dx' n ' dx' n ' 



FT 



da'^ , de^ 



— — ^a'^lna: -; — =e^. 

 dx dx 



•"f" 1, dlnx 1 



dsinx dcosx . dtgx 1 dcotg 1 



—5 — r^cosx;—^ — = — sinx; -T — = — —; = ^^. 



dx dx . dx cos-x dx sin-x 



darcsinx _ 1 darccosx _ 1 darctgx_ 1 



dx "pi^^"' d^^ ~ ~ [/Tz::^ ' dx ~l + x2 



d arc cotg x 1 



dx l+x^ 



^ = 0; :^a.f(x) = 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 f(x)^ g(x)f(x)-f(x).g-(x) 

 dxg(x) [g(x)]-^ 



Einführung neuer Variablen. 



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

 dy dv du dv dv du dv 

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



dlnf(x) _f^(x) 

 dx ~ f (x) • 



