Given
A function
f
(
x
)
=
6
x
5
−
12
x
4
+
12
x
2
−
6
x
+
4
.
Differentiate the function with respect to
x
,
f
′
(
x
)
=
d
d
x
(
6
x
5
−
12
x
4
+
12
x
2
−
6
x
+
4
)
=
6
(
5
x
4
)
−
12
(
4
x
3
)
+
12
(
2
x
)
−
6
=
30
x
4
−
48
x
3
+
24
x
−
6
Again, differentiate
f
′
(
x
)
with respect to
x
,
d
d
x
(
f
′
(
x
)
)
=
d
d
x
(
30
x
4
−
48
x
3
+
24
x
−
6
)
f
′′
(
x
)
=
30
(
4
x
3
)
−
48
(
3
x
2
)
+
24
=
120
x
3
−
144
x
2
+
24
Again, differentiate
f
′′
(
x
)
with respect to
x
,
d
d
x
(
f
′′
(
x
)
)
=
d
d
x
(
120
x
3
−
144
x
2
+
24
)
f
′′′
(
x
)
=
120
(
3
x
2
)
−
144
(
2
x
)
=
360
x
2
−
288
x
Therefore, the third derivative of the given function is,
f
′′′
(
x
)
=
360
x
2
−
288
x
.