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Byju's Answer
Standard XII
Physics
Chain Rule of Differentiation
Find the deri...
Question
Find the derivative of
y
with respect to
x
at
x
=
1
, where function
y
is expressed as
y
=
√
x
3
+
1
.
A
1
2
√
2
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B
3
√
2
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C
3
√
2
√
5
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D
3
2
√
2
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Solution
The correct option is
D
3
2
√
2
We have,
y
=
√
x
3
+
1
let
μ
(
x
)
=
x
3
+
1
∴
y
=
√
μ
,
d
y
d
μ
=
1
2
√
μ
and we know from chain rule:
d
y
d
x
=
d
y
d
μ
.
d
μ
d
x
and
d
μ
d
x
=
d
d
x
(
x
3
+
1
)
=
3
x
2
⇒
d
y
d
x
=
3
x
2
2
√
x
3
+
1
At
(
x
=
1
)
⇒
d
y
d
x
=
3
×
1
2
2
√
1
3
+
1
=
3
2
√
2
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Similar questions
Q.
Find the derivative of
y
with respect to
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