Question

Differentiate
log x/x​

Answer 1

Step-by-step explanation:

Let

y

=

(

ln

x

)

x

Then taking natural logarithms on both sides,

ln

y

=

ln

(

ln

x

)

x

⇒

ln

y

=

x

ln

(

ln

x

)

Differentiating both sides,

1

y

d

y

d

x

=

ln

(

ln

x

)

+

x

ln

x

d

d

x

ln

x

⇒

d

y

d

x

=

y

[

ln

(

ln

x

)

+

x

ln

x

1

x

]

⇒

d

y

d

x

=

(

ln

x

)

x

[

ln

(

ln

x

)

+

1

ln

x

]

Answer 2

Answer:

$\frac{d}{dx} (\frac{log x }{x} )$

use divide formula

$\frac{x \frac{d (log x)}{dx} - log x \frac{d(x)}{dx} }{x^{2} }$

Step-by-step explanation:

x * 1/x - log x *1 / x^2

1 -log x / x^2

answer