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Mathematics
Problem
d
d
x
[
log
sin
e
x
]
=
\frac{d}{dx} \left[ \log \sqrt{\sin \sqrt{e^x}} \right] =
d
x
d
[
lo
g
sin
e
x
]
=
(a)
1
4
e
x
/
2
cot
(
e
x
/
2
)
\frac{1}{4} e^{x/2} \cot(e^{x/2})
4
1
e
x
/2
cot
(
e
x
/2
)
(b)
e
x
/
2
cot
(
e
x
/
2
)
e^{x/2} \cot(e^{x/2})
e
x
/2
cot
(
e
x
/2
)
(c)
1
4
e
x
cot
(
e
x
)
\frac{1}{4} e^x \cot(e^x)
4
1
e
x
cot
(
e
x
)
(d)
1
2
e
x
/
2
cot
(
e
x
/
2
)
\frac{1}{2} e^{x/2} \cot(e^{x/2})
2
1
e
x
/2
cot
(
e
x
/2
)
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