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Mathematics
Mathematics
Problem
If
y
=
(
1
+
x
)
x
y = (1 + x)^x
y
=
(
1
+
x
)
x
, then
d
y
d
x
=
\frac{dy}{dx} =
d
x
d
y
=
(a)
(
1
+
x
)
x
[
x
1
+
x
+
log
e
x
]
(1 + x)^x \left[ \frac{x}{1 + x} + \log e x \right]
(
1
+
x
)
x
[
1
+
x
x
+
lo
g
e
x
]
(b)
x
1
+
x
+
log
(
1
+
x
)
\frac{x}{1 + x} + \log(1 + x)
1
+
x
x
+
lo
g
(
1
+
x
)
(c)
(
1
+
x
)
x
[
x
1
+
x
+
log
(
1
+
x
)
]
(1 + x)^x \left[ \frac{x}{1 + x} + \log(1 + x) \right]
(
1
+
x
)
x
[
1
+
x
x
+
lo
g
(
1
+
x
)
]
(d) None of these
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