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} \cdot 1

Simplify

= \frac{1}{1 + x}