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Mathematics
Mathematics
Problem
If
y
=
log
x
⋅
e
(
tan
x
+
x
2
)
y = \log x \cdot e^{(\tan x + x^2)}
y
=
lo
g
x
⋅
e
(
t
a
n
x
+
x
2
)
, then
d
y
d
x
=
\frac{dy}{dx} =
d
x
d
y
=
(a)
e
(
tan
x
+
x
2
)
[
1
x
+
(
sec
2
x
+
x
)
log
x
]
e^{(\tan x + x^2)} \left[ \frac{1}{x} + (\sec^2 x + x) \log x \right]
e
(
t
a
n
x
+
x
2
)
[
x
1
+
(
sec
2
x
+
x
)
lo
g
x
]
(b)
e
(
tan
x
+
x
2
)
[
1
x
+
(
sec
2
x
−
x
)
log
x
]
e^{(\tan x + x^2)} \left[ \frac{1}{x} + (\sec^2 x - x) \log x \right]
e
(
t
a
n
x
+
x
2
)
[
x
1
+
(
sec
2
x
−
x
)
lo
g
x
]
(c)
e
(
tan
x
+
x
2
)
[
1
x
+
(
sec
2
x
+
2
x
)
log
x
]
e^{(\tan x + x^2)} \left[ \frac{1}{x} + (\sec^2 x + 2x) \log x \right]
e
(
t
a
n
x
+
x
2
)
[
x
1
+
(
sec
2
x
+
2
x
)
lo
g
x
]
(d)
e
(
tan
x
+
x
2
)
[
1
x
+
(
sec
2
x
−
2
x
)
log
x
]
e^{(\tan x + x^2)} \left[ \frac{1}{x} + (\sec^2 x - 2x) \log x \right]
e
(
t
a
n
x
+
x
2
)
[
x
1
+
(
sec
2
x
−
2
x
)
lo
g
x
]
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