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Byju's Answer
Standard XII
Mathematics
Chain Rule of Differentiation
If a=x y p-...
Question
If
a
=
x
y
p
−
1
,
b
=
x
y
q
−
1
and
c
=
x
y
r
−
1
,
prove that
a
q
−
r
b
r
−
p
c
p
−
q
=
1
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Solution
Given:
a
=
x
y
p
−
1
,
b
=
x
y
q
−
1
and
c
=
x
y
r
−
1
,
LHS
=
a
q
−
r
b
r
−
p
c
p
−
q
=
(
x
y
p
−
1
)
q
−
r
(
x
y
q
−
1
)
r
−
p
(
x
y
r
−
1
)
p
−
q
=
x
q
−
r
+
r
−
p
+
p
−
q
y
q
p
+
r
−
q
−
p
r
+
q
r
+
p
−
q
p
−
r
+
p
r
+
q
−
p
−
q
r
=
x
0
y
0
=
1
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4
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