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Byju's Answer
Standard XII
Mathematics
Chain Rule of Differentiation
If ey x + 1...
Question
If
e
y
(
x
+
1
)
=
1
, then show that
d
2
y
d
x
2
=
(
d
y
d
x
)
2
.
Open in App
Solution
e
y
(
x
+
1
)
=
1
e
y
×
1
+
[
e
y
×
d
y
d
x
×
(
x
+
1
)
]
=
0
Differentiating on both sides
⇒
d
y
d
x
=
−
e
y
e
y
×
(
x
+
1
)
=
−
1
x
+
1
Differentiating again
⇒
d
2
y
d
x
2
=
−
1
−
(
x
+
1
)
2
=
1
(
x
+
1
)
2
⇒
d
2
y
d
x
2
=
1
(
x
+
1
)
2
=
(
−
1
x
+
1
)
2
=
(
d
y
d
x
)
2
Hence proved
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0
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Chain Rule of Differentiation
Standard XII Mathematics
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