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3 votes
Find the third derivative of the function y=6x-x2/x2

1 Answer

2 votes
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
.

User Adam Morris
by
3.9k points