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Question
Mathematics
If xy=ex-y, then (d y/d x) is equal to
Q. If
x
y
=
e
x
−
y
, then
d
x
d
y
is equal to
1835
184
Manipal
Manipal 2010
Report Error
A
(
1
+
l
o
g
x
)
2
l
o
g
x
B
(
1
+
l
o
g
x
)
x
−
y
C
(
1
+
l
o
g
x
)
2
x
−
y
D
(
1
+
l
o
g
x
)
1
Solution:
We have,
x
y
=
e
x
−
y
⇒
y
lo
g
x
=
(
x
−
y
)
lo
g
e
=
x
−
y
⇒
y
=
1
+
l
o
g
x
x
⇒
d
x
d
y
=
(
1
+
l
o
g
x
)
2
(
1
+
l
o
g
x
)
⋅
1
−
x
⋅
x
1
=
(
1
+
l
o
g
x
)
2
l
o
g
x