Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Mathematics
Mathematics
Problem
Let the derivative of
f
(
x
)
f(x)
f
(
x
)
be defined as
D
∗
f
(
x
)
=
lim
h
→
0
f
2
(
x
+
h
)
−
f
2
(
x
)
h
D^* f(x) = \lim_{h \to 0} \frac{f^2(x+h) - f^2(x)}{h}
D
∗
f
(
x
)
=
lim
h
→
0
h
f
2
(
x
+
h
)
−
f
2
(
x
)
, where
f
2
(
x
)
=
{
f
(
x
)
}
2
f^2(x) = \{f(x)\} ^2
f
2
(
x
)
=
{
f
(
x
)
}
2
. If
u
=
f
(
x
)
u = f(x)
u
=
f
(
x
)
,
v
=
g
(
x
)
v = g(x)
v
=
g
(
x
)
, then the value of
D
∗
(
u
v
)
D^*\left(\frac{u}{v}\right)
D
∗
(
v
u
)
is a.
u
2
(
D
∗
v
)
−
v
2
(
D
∗
u
)
v
4
\frac{u^2(D^*v) - v^2(D^*u)}{v^4}
v
4
u
2
(
D
∗
v
)
−
v
2
(
D
∗
u
)
b.
u
(
D
∗
v
)
−
v
(
D
∗
u
)
v
2
\frac{u(D^*v) - v(D^*u)}{v^2}
v
2
u
(
D
∗
v
)
−
v
(
D
∗
u
)
c.
v
2
(
D
∗
u
)
−
u
2
(
D
∗
v
)
v
4
\frac{v^2(D^*u) - u^2(D^*v)}{v^4}
v
4
v
2
(
D
∗
u
)
−
u
2
(
D
∗
v
)
d.
v
(
D
∗
u
)
−
u
(
D
∗
v
)
v
2
\frac{v(D^*u) - u(D^*v)}{v^2}
v
2
v
(
D
∗
u
)
−
u
(
D
∗
v
)
Browse the problem library