Differentiate ln(x)/x

To differentiate this, we use the quotient rule as we have 2 functions of x as a fraction.

The quotient rule states that:

where u is the numerator function and v is the denominator function.

Therefore, u=ln x and v=x.

So:

as that is the derivative of ln x.

And:

as that is the derivative of x.

Substituting these values into the quotient rule equation we have the following answer to this question: