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MHT CET 2018 Math Solved Paper
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© examsnet.com
Question : 4
Total: 50
If
log
10
(
x
3
−
y
3
x
3
+
y
3
)
= 2 then
d
y
d
x
=
x
y
-
y
x
-
x
y
y
x
Validate
Solution:
(d) Since,
log
10
(
x
3
−
y
3
x
3
+
y
3
)
= 2
∴
log
(
x
3
−
y
3
)
−
log
(
x
3
+
y
3
)
= 2
⇒
log
(
x
3
−
y
3
)
= 2 +
log
(
x
3
+
y
3
)
Differentiating b/s w.r.t. x
⇒
1
x
3
−
y
3
[
3
x
2
−
3
y
2
dy
dx
]
=
1
x
3
+
y
3
[
3
x
2
+
3
y
2
dy
d
x
]
⇒
3
x
2
x
3
−
y
3
−
3
y
2
x
3
−
y
3
d
y
d
x
=
3
x
2
x
3
+
y
3
+
3
y
2
x
3
+
y
3
d
y
d
x
⇒
3
x
2
x
3
−
y
3
−
3
x
2
x
3
+
y
3
=
[
3
y
2
x
3
+
y
3
+
3
y
2
x
3
−
y
3
]
d
y
d
x
⇒
3
x
2
[
1
x
3
−
y
3
−
1
x
3
+
y
3
]
=
3
y
2
[
1
x
3
+
y
3
+
1
x
3
−
y
3
]
d
y
d
x
⇒
3
x
2
[
2
y
3
(
x
3
−
y
3
)
(
x
3
+
y
3
)
]
=
3
y
2
[
2
x
3
(
x
3
+
y
3
)
(
x
3
−
y
3
)
]
d
y
d
x
⇒
y
x
=
d
y
d
x
© examsnet.com
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