Question 25 - Week 8 Practice | Prasnya
Prasnya
Continue with Google
Practice path
Dashboard
Exam
Quiz 2
Go to subject
Mathematics 1
Go to chapter
Week 8
Question 25
00:00
Est. 3 min
Marks:
+3.00
0.00
Passage
Consider three differentiable functions
f
(
x
)
f(x)
,
g
(
x
)
g(x)
and
h
(
x
)
h(x)
such that
f
(
x
)
=
g
(
2
x
2
+
x
)
h
(
3
x
3
+
x
)
f(x)=g(2x^2+x)h(3x^3+x)
,
g
′
(
0
)
=
g
(
0
)
=
3
g'(0)=g(0)=3
, and
h
′
(
0
)
=
h
(
0
)
=
1
h'(0)=h(0)=1
. Use this information to answer the subquestions.
Question
Which of the following options is/are true?
Comprehension
Medium Difficulty
06 August 2023
A
f
′
(
x
)
=
(
4
x
+
1
)
(
9
x
2
+
1
)
g
′
(
2
x
2
+
x
)
h
′
(
3
x
3
+
x
)
f'(x)=(4x+1)(9x^2+1)g'(2x^2+x)h'(3x^3+x)
.
B
f
′
(
x
)
=
(
4
x
+
1
)
g
′
(
2
x
2
+
x
)
h
(
3
x
3
+
x
)
+
(
9
x
2
+
1
)
g
(
2
x
2
+
x
)
h
′
(
3
x
3
+
x
)
f'(x)=(4x+1)g'(2x^2+x)h(3x^3+x)+(9x^2+1)g(2x^2+x)h'(3x^3+x)
.
C
f
′
(
0
)
=
2
g
′
(
0
)
h
(
0
)
f'(0)=2g'(0)h(0)
.
D
f
(
0
)
=
g
(
0
)
h
(
0
)
f(0)=g(0)h(0)
.