( f ± g) 0 = f 0 ± g0
( f · g) 0 = f 0 · g + f · g0
à !
f
f 0 · g − f · g0
=
g
g 2
( c) 0 = 0
( c · f ) 0 = c · f 0
( xr) 0 = rxr− 1
(sin x) 0 = cos x
(cos x) 0 = − sin x
1
( tgx) 0 = cos2 x 1
( ctgx) 0 = − sin2 x
( ax) 0 = ax · ln a
( ex) 0 = ex
1
1
(log a x) 0 =
·
x ln a
1
(ln x) 0 = x 1
(arcsin x) 0 = √ 1 − x 2
1
(arccos x) 0 = −√ 1 − x 2
1
( arctgx) 0 = 1 + x 2
1
( arcctgx) 0 = − 1 + x 2
(sinh x) 0 = cosh x
(cosh x) 0 = sinh x
1