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

1 Answer

sciencesolve's profile pic

sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted on

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

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

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

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

`f'(x) = -x/(x^2)`

Reducing like terms, yields:

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

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