Download - Lista_5_CDI_1_2012_01
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y′ = f ′(x), y = f (x)
y = (4x3 − 5x2 + 2x + 1)3
y = elnx
y = ln((2 − 3x)5)
y = ln3(5x2 + 1)
y = (x3 − 2x)
y =
1
x2 + x2
4
y =
4
(x8 − x5 + 6)10
y = 1
ln x + ln
1
x
y = x2 − 2x3− 4x
33
y = ln
3
√ x2 − 1x2 + 1
y = ln(ln(
(2x)))
y = (sin(5x) − cos(5x))5
y =
(3x)
x3 + 1
y = tan(x2
)cos(x2
)
y = y = ln
ex + 1
ex − 1
x ln y − y ln x = 1
exy − x3 + 3y2 = 11
8x2 + y2 = 10
y = x sin y
x = sin
1
y
y = 3arcsin(x
3)
(y2 − 9)4 = (4x2 + 3x− 1)2
cos2(3yx)
−ln(xy) = 0
y = (1 + arccos(3x))3
y = ln(arctan(x2))
y2 = e−3x √
x
y = arctan(3x− 5)
y = arcsin(
√ x)
x2 + xy + y2 = 3
r : x + y = 1
(x2 + 4) y = 4x− x3
4y3−x2y−x + 5y = 0
x4−4y3 + 5x + y = 0
x = a y = x3
3 + 4x + 3 P y = 2x2 + x
Q a
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C : xy2 + y3 = 2x−2y +2
P
C 1 : 2x
2 + 3y2 = 5 C 1 : y
2 = x3
C 1 C 2 P
f
(x
) =
1
x,
f (n)
(x
)
n
f (n)
(1)?
n
f (x) = eax,
a ∈ R∗.
f (x) = (a + bx)m, a, b ∈ R∗ m ∈ N∗
f (x) = x
x + 1
f (x) = ln(2x − 3)
f : R
→ R
g : R
→ R
g(x) = f (x +
2cos(3x)).
g′′(x).
f ′(2) = 1 f ′′(2) = 8, g′′(0).
g (x) = cos x. [f (x)]2 ,
f : R → R
f (0) = −1 f ′ (0) = f ” (0) = 2, g′′ (0) .
f ′ (0) f
sin x−√ 32
= f (3x − π) + 3x− π.
g (f ◦ g)′ (x) = 24x + 34, f (x) = 3x2 − x− 1 g′ (x) = 2.
(g ◦ f ◦ h)′ (2) , f (0) = 1, h (2) = 0, g′ (1) = 5 f ′ (0) = h′ (2) = 2. k y(x) = k (x) (x)
yy ′ + (x) 2(x) = 0.
A
B
y = A sin(2x) + B cos(2x)
y′′ + y′ − 2y = sin(2x).
C
C
P (1,√ 3)
r
P.
y = sinh(u) ⇒ y′ = u′ cosh(u);
y = cosh(u) ⇒ y′ = u′ sinh(u);
y =
(u) ⇒ y′ = u′
2(u);
y =
(u) ⇒ y′ = −u′
2(u);
y = (u)
⇒ y′ =
−u′ (u) (u);
y = (u) ⇒ y′ = −u′ (u) (u);
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y = arcsin(u) ⇒ y′ = u
′√
1− u2
y = arccos(u) ⇒ y′ = − u
′√
1 − u2
y = arctan(u) ⇒ y′ = u
′
1 + u2
y =
(u) ⇒ y′ = − u
′
1 + u2
y =
(u) ⇒ y′ = u′
|u|√ u2 − 1
y =
(u) ⇒ y′ = − u′
|u|√ u2 − 1
y′ = 6(6x2 − 5x + 1)(4x3 − 5x2 + 2x + 1)2
y′ = 1
y′ = 15
3x− 2
y′ =
30x ln2(5x2 + 1)
5x2 + 1
y′ = (3x2 − 2) 2(x3 − 2x)
y′ = 8(x4 − 1)(x4 + 1)3
x9
y′ =
−40x4(8x3 − 5)(x8 − x5 + 6)11
y′ = − 1x ln2 x
− 1x
y′ = 6(x − 2)2x2(2x4 − 8x3 + 3x − 3)
(3 − 4x3
)4
y′ =
4x
3(x4 − 1) y′ =
2 tan(2x)
ln(sec(2x))
y′ = 25(sin(5x) − cos(5x))4(sin(5x) + cos(5x))
y′ = −3 (3x)[ (3x)(x
3 + 1) + x2]
(x3 + 1)2
y′ = 2x cos(x2
)
y′ = − 2e
x
e2x − 1
y′ = y(y − x ln y)x(x− y ln x)
y′ = 3x2 − yexy
6y + xexy
y′ = −8x
y
y′ = sin y1 − x cos y
y′ = −y2 sec
1
y
y′ = 3x2 ln(3)3arcsin(x
3)
√ 1− x6
y′ = (4x2 + 3x− 1)(8x + 3)
4(y2 − 9)3
y′ =
−y
x
y′ = −9(1 + arccos(3x))2
√ 1 − 9x2
y′ =
2x
arctan(x2)(1 + x4)
y′ = e−3x[−6√ x tan(√ x) + sec2(√ x)]
4y√
x
y′ = 3
9x2 − 30x + 26 y′ =
1
2√ x− x2 y = −x− 2 y = −x + 2
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y = −x
m1 =
1
5 m2 = −5
a = 1 : y = 5x +
7
3 y = 5x− 2;
a = 3 : y = 13x− 5
y = 13x − 18.
y = −7x + 8
m1 = ±23
m2 = ∓32
f (n)(x) =
(−1)nn!xn+1
f (n)(1) = (−1)nn!
f (n)(x) = aneax
f (n)(x) = m(m
−1)(m
−2)
· · ·(m
−(n
−1))(a + bx)m−nbn, n
≤m f (n)(x) = 0, n > m
f (n)(x) = (−1)n+1n!(x + 1)n+1
f (n)(x) =
(−1)n−12n(n − 1)!(2x − 3)n
g′′(x) = f ′′(x + 2 cos(3x))(1 − 6 sin(3x))2 − 18 cos(3x)f ′(x + 2 cos(3x)) g′′(0) = −10
g′′(0) = 3
f ′(0) =
−6
5
g(x) = 2x + 3
k = −1 k = 1.
A = − 3
20 B = − 1
20
mt = −√
3
3 mr =
√ 3.