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Mathematics
Mathematics
Problem
Let
y
y
y
be a differentiable function of
x
x
x
satisfying
ln
(
x
y
)
=
x
2
\ln(xy)=x^{2}
ln
(
x
y
)
=
x
2
for
x
>
0
x>0
x
>
0
and
y
>
0
y>0
y
>
0
. What is
d
y
d
x
\dfrac{dy}{dx}
d
x
d
y
at the point
(
1
,
e
)
(1,e)
(
1
,
e
)
? a)
2
e
2e
2
e
b)
e
e
e
c)
1
1
1
d)
e
2
e^{2}
e
2
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