What is the derivative of y=(ln x)/x?

Rigoberto Mann

Rigoberto Mann

Answered question

2023-03-07

What is the derivative of y ln x x ?

Answer & Explanation

Nick Osborn

Nick Osborn

Beginner2023-03-08Added 3 answers

Use the quotient rule, which states that
d d x [ f ( x ) g ( x ) ] = f ( x ) g ( x ) - g ( x ) f ( x ) [ g ( x ) ] 2
Applying this to y = ln x x , we see that
y = x d d x [ ln x ] - ln x d d x [ x ] x 2
Since d d x [ ln x ] = 1 x and d d x [ x ] = 1 ,
y = x ( 1 x ) - ln x x 2
y = 1 - ln x x 2

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