Ingenieria Electronica

55)
x + 1
g·x = ·(2·x - 5)
x + 2
d ⎛ x + 1 ⎞
⎯⎯ ⎜g·x = 2·x - 5)⎟
dx ⎝ x + 2 ⎠2·x2 + 8·x - 1
g =
(x + 2) 2


56)
x2 - x - 3
f·x = ·(x2 + x + 1)
x2 + 1

⎛⎞
d ⎜ x2 - x - 3 ⎟
⎯⎯ ⎜f·x = ·(x2 + x + 1)⎟
dx ⎝ x2 + 1 ⎠2·(x5 + 2·x3 + 2·x2 - 2)
f =
(x2 + 1) 2


57)

θ
g·θ =
1 - SIN(θ)

d ⎛ θ ⎞
⎯⎯ ⎜g·θ =
dθ ⎝1 - SIN(θ) ⎠

θ·COS(θ) - SIN(θ) + 1
g =
(SIN(θ) - 1) 2

59)

SIN(θ)
f·θ =
1 - COS(θ)



d ⎛SIN(θ) ⎞
⎯⎯ ⎜f·θ = ⎟
dθ ⎝ 1 - COS(θ) ⎠

1
f =
COS(θ) – 1


59)

1 + CSC(x)
y =
1 - CSC(x)

d⎛ 1 + CSC(x) ⎞
⎯⎯ ⎜y = ⎟
dx ⎝ 1 - CSC(x) ⎠

2·COS(x)
y = -
(SIN(x) - 1) 2

⎛ π ⎞
2·COS ⎜⎟
⎝ 6 ⎠
y = -
⎛ ⎛ π ⎞ ⎞2
⎜SIN ⎜ ⎟ - 1 ⎟
⎝ ⎝ 6 ⎠ ⎠

[pic]



60)

f·x = TAN(x)·COT(x)d
⎯⎯ (f·x = TAN(x)·COT(x))
dx

f = 0

[pic]

61)

SEC(t)
h·t =
t

d ⎛ SEC(t) ⎞
⎯⎯ ⎜h·t = ⎟
dt ⎝ t ⎠SIN(t) 1
h = -
t·COS(t) 2 t ·COS(t) 2

SIN(π) 1
π = -
π·COS(π)...