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Mathematics
Mathematics
Problem
For the implicit relation
x
y
=
y
x
x^{y}=y^{x}
x
y
=
y
x
, compute
d
y
d
x
\dfrac{dy}{dx}
d
x
d
y
at the point
(
2
,
2
)
(2,2)
(
2
,
2
)
. a)
ln
2
−
1
ln
2
\displaystyle\frac{\ln 2-1}{\ln 2}
ln
2
ln
2
−
1
b)
1
1
1
c)
0
0
0
d)
ln
2
ln
2
−
1
\displaystyle\frac{\ln 2}{\ln 2-1}
ln
2
−
1
ln
2
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