187k views
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
8.1k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories