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Mathematics
Problem
Let
f
(
x
)
=
x
e
x
tan
x
f(x)=x e^{x}\tan x
f
(
x
)
=
x
e
x
tan
x
for all real
x
x
x
in the domain of
tan
x
\tan x
tan
x
. (a) Calculate
f
′
(
x
)
f'(x)
f
′
(
x
)
, expressing your answer as a single simplified analytical expression. (b) Determine the exact value of
f
′
(
0
)
f'(0)
f
′
(
0
)
.
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