Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Let
d
d
x
f
(
x
)
=
sin
12
x
−
cos
12
x
(
sin
2
x
−
cos
2
x
)
(
1
−
3
sin
2
x
cos
2
x
)
\frac{d}{dx} f(x) = \frac{\sin^{12} x - \cos^{12} x}{(\sin^2 x - \cos^2 x)(1 - 3 \sin^2 x \cos^2 x)}
d
x
d
f
(
x
)
=
(
s
i
n
2
x
−
c
o
s
2
x
)
(
1
−
3
s
i
n
2
x
c
o
s
2
x
)
s
i
n
12
x
−
c
o
s
12
x
…
Mathematics
Problem
Let
d
d
x
f
(
x
)
=
sin
12
x
−
cos
12
x
(
sin
2
x
−
cos
2
x
)
(
1
−
3
sin
2
x
cos
2
x
)
\frac{d}{dx} f(x) = \frac{\sin^{12} x - \cos^{12} x}{(\sin^2 x - \cos^2 x)(1 - 3 \sin^2 x \cos^2 x)}
d
x
d
f
(
x
)
=
(
s
i
n
2
x
−
c
o
s
2
x
)
(
1
−
3
s
i
n
2
x
c
o
s
2
x
)
s
i
n
12
x
−
c
o
s
12
x
be such that
f
(
0
)
=
0
f(0) = 0
f
(
0
)
=
0
then
f
(
π
2
)
f\left(\frac{\pi}{2}\right)
f
(
2
π
)
equals
k
π
16
\frac{k\pi}{16}
16
k
π
. Find the value of
k
(
k
∈
N
)
k\,(k \in \mathbb{N})
k
(
k
∈
N
)
Browse the problem library