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Mathematics
Mathematics
Problem
Let
f
f
f
be a differentiable function satisfying
[
f
(
x
)
]
n
=
f
(
n
x
)
for all
x
∈
R
[f(x)]^n = f(nx) \text{ for all } x \in \mathbb{R}
[
f
(
x
)
]
n
=
f
(
n
x
)
for all
x
∈
R
Then,
f
′
(
x
)
f
(
n
x
)
f'(x)f(nx)
f
′
(
x
)
f
(
n
x
)
equals a.
f
(
x
)
f(x)
f
(
x
)
b. 0 c.
f
(
x
)
f
′
(
n
x
)
f(x)f'(nx)
f
(
x
)
f
′
(
n
x
)
d. None of these
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