U' + V' (U * V)' = U' * V + U * V' - VTS NS
U' + V' (U * V)' = U' * V + U * V' - VTS NS
U' + V' (U * V)' = U' * V + U * V' - VTS NS
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Pravila diferenciranja<br />
(c)' = 0<br />
(U + V)' = <strong>U'</strong> + <strong>V'</strong><br />
(U * V)' = <strong>U'</strong> * V + U * <strong>V'</strong><br />
(C*V)' = C * <strong>V'</strong><br />
( U V )' =<br />
V(U(x))' = V u ' * <strong>U'</strong><br />
U '∗V −U∗V '<br />
V 2<br />
Tablica izvoda elementarnih funkcija<br />
(x)' = 1<br />
(x n )' = n(x n-1 )<br />
(a x )' = a x lna<br />
(e x )' = e x<br />
( log a<br />
(x ) )' =<br />
(lnx)' =<br />
1<br />
x∗lna<br />
1<br />
x<br />
(sinx)' = cosx<br />
(cosx)' = - sinx<br />
(tgx)' =<br />
(ctgx)' = -<br />
(arcsinx)' =<br />
(arccosx)' = -<br />
1<br />
cos 2 x<br />
1<br />
sin 2 x<br />
1<br />
√1−x 2<br />
1<br />
√1−x 2
y ↑ y' > 0<br />
y ↓ y' < 0<br />
(arctgx)' =<br />
(arcctgx)' = -<br />
( √ x )' =<br />
( 3 √ x )' =<br />
( a x )' = -<br />
1<br />
1+x 2<br />
1<br />
1+x 2<br />
1<br />
2√x<br />
1<br />
3 3 √x 2<br />
1<br />
x 2<br />
Monotonost i ekstremi<br />
f U f '' (x) > 0<br />
Konveksnost-konkavnost i prevoji<br />
f ∩ f '' (x) < 0