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UPSEE 2019 Solved Paper
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© examsnet.com
Question : 118
Total: 150
Suppose
f
is differentiable function such that
f
(
g
(
x
)
)
=
x
2
and
f
′
(
x
)
=
1
+
(
f
(
x
)
)
2
, then the value of
g
′
(
2
)
is
1
17
2
17
3
17
4
17
Validate
Solution:
We have,
f
(
g
(
x
)
=
x
2.
∴
f
′
(
g
(
x
)
.
g
′
(
x
)
=
2
x
g
′
(
x
)
=
2
x
f
′
(
g
(
x
)
)
;
g
′
(
x
)
=
2
x
1
+
(
f
(
g
x
)
)
2
[
∵
f
′
(
x
)
=
1
+
(
f
(
x
)
)
2
]
g
′
(
x
)
=
2
x
1
+
x
4
g
′
(
2
)
=
4
1
+
16
=
4
17
© examsnet.com
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