a)

b)

c)

d)

e)

f)

fa(x) = If[0 ≤ x ≤ (2 * π), sin(x)]
fa'(x) = fa'(x)
fb(x) = If[(-2 * π) ≤ x ≤ (2 * π), x - cos(x)]
fb'(x) = fb'(x)
fc(x) = If[(-π) ≤ x ≤ π, (0.5 * cos((2 * x))) - x]
fc'(x) = fc'(x)
fd(x) = If[-6 ≤ x ≤ 6, (-cos((π / 4 * x)))]
fd'(x) = fd'(x)
fe(x) = If[0 ≤ x ≤ 12, (2 * sin((π / 6 * x)))]
fe'(x) = fe'(x)
ff(x) = If[-2 ≤ x ≤ 2, (-4 * cos((4 / π * x)))]
ff'(x) = ff'(x)
a = false
b = false
c = false
d = false
e = false
f = false