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Byju's Answer
Standard XII
Mathematics
Geometrical Interpretation
Let g x be an...
Question
Let g(x) be an antiderivative for f(x). Then In
(
1
+
(
g
(
x
)
)
2
)
is an antiderivate for
A
2
f
(
x
)
g
(
x
)
1
+
(
f
(
x
)
)
2
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B
2
f
(
x
)
g
(
x
)
1
+
(
g
(
x
)
)
2
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C
2
f
(
x
)
1
+
(
f
(
x
)
)
2
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D
None
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Solution
The correct option is
B
2
f
(
x
)
g
(
x
)
1
+
(
g
(
x
)
)
2
Given
∫
f
(
x
)
d
x
=
g
(
x
)
g
′
(
x
)
=
f
(
x
)
Now
d
d
x
(
I
n
(
1
+
g
2
(
x
)
)
=
2
g
(
x
)
g
′
(
x
)
1
+
g
2
(
x
)
2
f
(
x
)
g
(
x
)
1
+
g
2
(
x
)
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0
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