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Standard XII
Mathematics
Higher Order Derivatives
Question
If
y
=
x
+
e
x
,
then
d
2
x
d
y
2
is equal to
−
e
x
(
1
+
e
x
)
2
−
e
x
(
1
+
e
x
)
3
e
x
1
(
1
+
e
x
)
2
A
−
e
x
(
1
+
e
x
)
2
B
e
x
C
1
(
1
+
e
x
)
2
D
−
e
x
(
1
+
e
x
)
3
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Solution
Verified by Toppr
y
=
x
+
e
x
Differentiating both sides w.r.t
x
,
we get:
⇒
d
y
d
x
=
1
+
e
x
Taking reciprocal on both sides,
⇒
d
x
d
y
=
1
1
+
e
x
---- ( 1 )
Differentiating both sides w.r.t.
y
,
we get:
⇒
d
2
x
d
y
2
=
−
e
x
(
1
+
e
x
)
2
d
x
d
y
From ( 1 ), we get:
⇒
d
2
x
d
y
2
=
−
e
x
(
1
+
e
x
)
3
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