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VITEEE 2014 Paper
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Section:
Mathematics
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© examsnet.com
Question : 82
Total: 120
If x .
d
y
d
x
+ y = x .
f
(
x
y
)
f
′
(
x
y
)
, then f (xy) is equal to
k
.
e
x
2
2
k
.
e
y
2
2
k
.
e
x
2
k
.
e
x
y
2
Validate
Solution:
x .
d
y
d
x
+ y = x .
f
(
x
y
)
f
′
(
x
y
)
i.e.
d
d
x
(xy) = x
f
(
x
y
)
f
′
(
x
y
)
⇒
f
′
(
x
y
)
f
(
x
y
)
d (xy) = x dx
⇒ ∫
f
′
(
x
y
)
f
(
x
y
)
d (xy) d (xy) = ∫ x dx
⇒ log [f (xy)] =
x
2
2
+ C
⇒ f (xy) =
e
(
x
2
∕
2
+
C
)
=
e
x
2
2
.
e
C
=
k
.
e
x
2
2
© examsnet.com
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