f (x) = 2 cos(x)
sec(x)
( ⇡3 , f ( ⇡3 )).
f 0 (x)
f (x) = e
ex
p
5x+3
ln(x)
(ex )0 = ex
(ln(x))0 = 1/x
✓
x
x=4
f
f (x) =
1
x
sin(x)
cos(x)
x
C(x) = 200 + 500x
C̄ =
800 ln(x)
C(x)
.
x
C̄min .
y0
y = x(
p
x2 )
x
x2 + 2xp + 8p2 = 2300
2 sin2 (3x)
x!0 1
cos(3x)
lim
F
F (x) =
x
1
f (x)
2
f
f (x) = cos2 (x) +
p
3 sin(x)
( ⇡/2, ⇡/2).
f (4n+2) (x)
f (x) = sin(x)
n = 0, 1, 2, . . .
g 0 ( 2)
g
f (x) = 3x3
f ( 1) =
f (x) = e2x ,
f
1
x
2
c
f
f (x) = x 6 sin(ln(x)) + 3 cos(ln(x))
f (x) = 3 x
3 ln
x
3
9
3
[4, 7].
f
g
f, g
g(x) =
g 0 (x) =
1
f (x)
1
f 0 (g(x))
f 00 (g(x))(g 0 (x))2 = f 0 (g(x))g 00 (x)
lim
x!0
sin(4x)
6|x|
r
1 + x2
1 x2
f (x) = 2 + 4(3
x)ex
f (x) = ln
2