What is the first d/(dt)(ln(2t)) ?

The first d/(dt)(ln(2t)) is 1/t

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d/(dt)(ln(2t))

\frac{d}{d t} (ln (2 t))

\frac{1}{t}

Solution steps

\frac{d}{d t} (ln (2 t))

Apply the chain rule:

\frac{1}{2 t} \frac{d}{d t} (2 t)

= \frac{1}{2 t} \frac{d}{d t} (2 t)

\frac{d}{d t} (2 t) = 2

= \frac{1}{2 t} \cdot 2

Simplify

\frac{1}{2 t} \cdot 2 : \frac{1}{t}

= \frac{1}{t}

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