B - Prírodovedecká fakulta - Univerzita Komenského
B - Prírodovedecká fakulta - Univerzita Komenského
B - Prírodovedecká fakulta - Univerzita Komenského
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⎛ 2<br />
⎜<br />
⎝ 5<br />
j. tan(<br />
5x)<br />
'<br />
⎞<br />
⎟ =<br />
⎠<br />
k. ( cotg(<br />
Sx)<br />
) '<br />
2<br />
5<br />
cos<br />
1<br />
2<br />
( 5x)<br />
'<br />
( 5x)<br />
( Sx)<br />
'<br />
( Sx)<br />
2<br />
= 2<br />
cos<br />
Lekcia 8 – Derivácie elementárnych funkcií<br />
( 5x)<br />
1<br />
− PS<br />
P = −P<br />
=<br />
2<br />
2<br />
sin<br />
sin<br />
l. ( 2 arcsin(<br />
x / 5)<br />
) '<br />
= 2<br />
5<br />
m. ( 1,<br />
1R<br />
arccos(<br />
W x ) '<br />
n. ( Aarctan(<br />
xB)<br />
) '<br />
2<br />
o. ( C arccotg(<br />
D x ) '<br />
1 −<br />
1<br />
= −1,<br />
1R<br />
A<br />
=<br />
1 +<br />
( xB)<br />
( x / 5)<br />
2<br />
− C<br />
=<br />
1 +<br />
2<br />
1 −<br />
( xB)<br />
'<br />
2 ( D x)<br />
2<br />
( x / 5)<br />
'<br />
1<br />
5 ( W x)<br />
( Sx)<br />
=<br />
2<br />
AB<br />
=<br />
1 +<br />
2 ( D x)<br />
'<br />
2<br />
5<br />
1<br />
1 − x<br />
2<br />
/ 25<br />
2<br />
5 −1,<br />
1RW<br />
( W x)<br />
' =<br />
4 2<br />
( ) 2<br />
xB<br />
− CD<br />
=<br />
1 +<br />
2<br />
( ) 2 2<br />
D x<br />
p. ( 6 sinh(<br />
2x)<br />
) ' = 6 cosh(<br />
2x)<br />
× ( 2x)<br />
' = 12 cosh(<br />
2x)<br />
'<br />
⎛<br />
⎞<br />
'<br />
⎛ x ⎞ ⎛ x ⎞ ⎛ x ⎞ 2,<br />
5 ⎛ x ⎞<br />
q. ⎜2,<br />
5cosh⎜<br />
⎟⎟<br />
= 2,<br />
5sinh⎜<br />
⎟ × ⎜ ⎟ = sinh⎜<br />
⎟<br />
⎝ ⎝ 8 ⎠⎠<br />
⎝ 8 ⎠ ⎝ 8 ⎠ 8 ⎝ 8 ⎠<br />
r. ( tanh(<br />
5x)<br />
) '<br />
8<br />
= 2<br />
cosh<br />
( 5x)<br />
'<br />
( 5x)<br />
40<br />
=<br />
cosh<br />
8 2<br />
s. ( cotgh(<br />
xG)<br />
) '<br />
− F<br />
=<br />
sinh<br />
( xG)<br />
'<br />
( xG)<br />
( 5x)<br />
− FG<br />
=<br />
sinh<br />
F 2<br />
2<br />
( xG)<br />
1 − W<br />
x<br />
85
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