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Byju's Answer
Standard XI
Mathematics
Differentiability
For some cons...
Question
For some constant
a
and
b
, find the derivative of the following functions:
(
a
x
2
+
b
)
2
.
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Solution
Let
f
(
x
)
=
(
a
x
2
+
b
)
2
⇒
f
(
x
)
=
a
2
x
4
+
2
a
b
x
2
+
b
2
∴
f
′
(
x
)
=
d
d
x
(
a
2
x
4
+
2
a
b
x
2
)
=
a
2
d
d
x
(
x
4
)
+
2
a
b
d
d
x
(
x
2
)
+
d
d
x
(
b
2
)
=
a
2
(
4
x
3
)
+
2
a
b
(
2
x
)
+
b
2
(
0
)
=
4
a
2
x
3
+
4
a
b
x
=
4
a
x
(
a
x
2
+
b
)
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Similar questions
Q.
For some constants
a
and
b
, find the derivative of
(i) (
x
ā
a
) (
x
ā
b
) (ii) (
ax
2
+
b
)
2
(iii)