What is the first (ln(1-x))^' ?

The first (ln(1-x))^' is -1/(1-x)

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(ln(1-x))^'

(ln (1 - x))^{^{'}}

- \frac{1}{1 - x}

Solution steps

(ln (1 - x))^{'}

Apply the chain rule:

\frac{1}{1 - x} (1 - x)^{'}

= \frac{1}{1 - x} (1 - x)^{'}

(1 - x)^{'} = - 1

= \frac{1}{1 - x} (- 1)

Simplify

= - \frac{1}{1 - x}