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KEAM 2011 Math Paper
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© examsnet.com
Question : 48
Total: 120
If
x
y
⋅
y
x
=
16
,
then
d
y
d
x
at
(
2
,
2
)
is
1
2
−
1
−
2
0
Validate
Solution:
x
y
y
x
=
16
Taking log on both sides,
y
log
x
+
x
log
y
=
log
16
Differentiating on both sides,
y
x
+
log
x
d
y
d
x
+
x
y
d
y
d
x
+
log
y
=
0
(
x
y
+
log
x
)
d
y
d
x
=
−
(
y
x
+
log
y
)
d
y
d
x
=
−
y
x
(
y
+
x
log
y
)
(
x
+
y
log
x
)
(
d
y
d
x
)
at
(
2
,
2
)
=
−
2
2
(
2
+
2
log
2
2
+
2
log
2
)
=
−
1
© examsnet.com
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