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Mathematics
Mathematics
Problem
Let
f
:
R
→
R
f: \mathbb{R} \to \mathbb{R}
f
:
R
→
R
be a differentiable function with
f
(
0
)
=
1
f(0) = 1
f
(
0
)
=
1
and satisfying the equation
f
(
x
+
y
)
=
f
(
x
)
f
′
(
y
)
+
f
′
(
x
)
f
(
y
)
for all
x
,
y
∈
R
.
f(x + y) = f(x)f'(y) + f'(x)f(y) \text{ for all } x, y \in \mathbb{R}.
f
(
x
+
y
)
=
f
(
x
)
f
′
(
y
)
+
f
′
(
x
)
f
(
y
)
for all
x
,
y
∈
R
.
Then, the value of
log
e
(
f
(
4
)
)
\log_e(f(4))
lo
g
e
(
f
(
4
))
is ________.
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