Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Mathematics
Mathematics
Problem
Let
f
(
x
)
=
ln
(
1
+
4
x
2
)
f(x)=\ln\!\left(\sqrt{1+4x^{2}}\,\right)
f
(
x
)
=
ln
(
1
+
4
x
2
)
. a. (i) Find
f
′
(
x
)
f'(x)
f
′
(
x
)
for general
x
x
x
. b. (ii) Hence, determine the exact value of
f
′
(
1
)
f'(1)
f
′
(
1
)
. c. (iii) Express your answer in the form
a
b
\dfrac{a}{b}
b
a
, where
a
a
a
and
b
b
b
are positive integers in their lowest terms.
Browse the problem library