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Standard XII
Mathematics
Question
If
x
m
.
y
n
=
(
x
+
y
)
m
+
n
, then
d
y
d
x
=
n
y
x
y
x
−
y
x
m
y
x
A
y
x
B
n
y
x
C
−
y
x
D
m
y
x
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Solution
Verified by Toppr
x
m
×
y
n
=
(
x
+
y
)
m
+
n
Taking log both sides we get
m
log
x
+
n
log
y
=
(
m
+
n
)
log
(
x
+
y
)
Differentiating w.r.t. x we get
m
x
+
n
y
d
y
d
x
=
m
+
n
x
+
y
(
1
+
d
y
d
x
)
⇒
d
y
d
x
(
n
y
−
m
+
n
x
+
y
)
=
m
+
n
x
+
y
−
m
x
⇒
d
y
d
x
(
n
x
+
n
y
−
m
y
−
n
y
y
(
x
+
y
)
)
=
m
x
+
n
x
−
m
x
−
m
y
x
(
x
+
y
)
⇒
d
y
d
x
=
(
n
x
−
m
y
n
x
−
m
y
)
y
x
=
y
x
⇒
d
y
d
x
=
y
x
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