Question

Calcular la derivada de $f(x)=\frac{log_{5} x}{x}$

Answer 1

Diferenciar utilizando la regla del cociente,
d
d
x
[
f
(
x
)
g
(
x
)
]
=
g
(
x
)
d
d
x
[
f
(
x
)
]
−
f
(
x
)
d
d
x
[
g
(
x
)
]
g
(
x
)
2
d
d
x
[
f
(
x
)
g
(
x
)
]
=
g
(
x
)
d
d
x
[
f
(
x
)
]
-
f
(
x
)
d
d
x
[
g
(
x
)
]
g
(
x
)
2
−
ln
(
5
)
log
5
(
x
)
+
1
x
2
ln
(
5
)
-
ln
(
5
)
log
5
(
x
)
+
1
x
2
ln
(
5
)