What is the first (ln(1+2x))^' ?

The first (ln(1+2x))^' is 2/(1+2x)

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(ln(1+2x))^'

(ln (1 + 2 x))^{^{'}}

\frac{2}{1 + 2 x}

Solution steps

(ln (1 + 2 x))^{'}

Apply the chain rule:

\frac{1}{1 + 2 x} (1 + 2 x)^{'}

= \frac{1}{1 + 2 x} (1 + 2 x)^{'}

(1 + 2 x)^{'} = 2

= \frac{1}{1 + 2 x} \cdot 2

Simplify

\frac{1}{1 + 2 x} \cdot 2 : \frac{2}{1 + 2 x}

= \frac{2}{1 + 2 x}

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