`y = 1/(ln(x))` Differentiate the function.

Expert Answers
sciencesolve eNotes educator| Certified Educator

You need to differentiate the function with respect to x, using the quotient rule, such that:

`f'(x) = (1/(ln x))'`

`f'(x) = (1'*(ln x) - 1*(ln x)')/(ln^2 x)`

`f'(x) = (0*ln x - 1/x)/(ln^2 x)`

`f'(x) = -1/(x*ln^2 x)`

Hence, evaluating the derivative of the given function, yields` f'(x) = -1/(x*ln^2 x).`

kalau eNotes educator| Certified Educator

 Differentiate the function.

Rewrite this as: 

`y=(lnx)^-1`

We can take the derivative by power rule and chain rule.  Chain rule is the derivative of the inner function.

`y'= -(ln(x))^-2 * (1/x)`

This simplifies to:  

`y'=-1/(x(lnx)^2)`

Access hundreds of thousands of answers with a free trial.

Start Free Trial
Ask a Question