Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Mathematics
Mathematics
Problem
If
y
=
tan
x
tan
2
x
tan
3
x
y = \tan x \tan 2x \tan 3x
y
=
tan
x
tan
2
x
tan
3
x
, then
d
y
d
x
\frac{dy}{dx}
d
x
d
y
has the value equal to a.
3
sec
2
3
x
tan
x
tan
2
x
+
sec
2
x
tan
2
x
tan
3
x
+
2
sec
2
2
x
tan
3
x
tan
x
3 \sec^2 3x \tan x \tan 2x + \sec^2 x \tan 2x \tan 3x + 2 \sec^2 2x \tan 3x \tan x
3
sec
2
3
x
tan
x
tan
2
x
+
sec
2
x
tan
2
x
tan
3
x
+
2
sec
2
2
x
tan
3
x
tan
x
b.
2
y
(
csc
2
x
+
2
csc
4
x
+
3
csc
6
x
)
2y (\csc 2x + 2 \csc 4x + 3 \csc 6x)
2
y
(
csc
2
x
+
2
csc
4
x
+
3
csc
6
x
)
c.
3
sec
2
3
x
−
2
sec
2
2
x
−
sec
2
x
3 \sec^2 3x - 2 \sec^2 2x - \sec^2 x
3
sec
2
3
x
−
2
sec
2
2
x
−
sec
2
x
d.
sec
2
x
+
2
sec
2
2
x
+
3
sec
2
3
x
\sec^2 x + 2 \sec^2 2x + 3 \sec^2 3x
sec
2
x
+
2
sec
2
2
x
+
3
sec
2
3
x
Browse the problem library