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KEAM 2014 Math Paper
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© examsnet.com
Question : 27
Total: 120
If
y
=
f
(
x
2
+
2
)
and
f
′
(
3
)
=
5
,
then
d
y
d
x
at
x
=
1
is
5
25
15
20
10
Validate
Solution:
Given,
y
=
f
(
x
2
+
2
)
On differentiating both sides w.r.t.
x
, we get
d
y
d
x
=
f
′
(
x
2
+
2
)
×
2
x
Put
x
=
1
,
we get
d
y
d
x
=
f
′
(
1
2
+
2
)
×
2
=
f
′
(
3
)
×
2
=
5
×
2
[
∵
f
′
(
3
)
=
5
given
]
=
10
© examsnet.com
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