What is the d/(dt)(ln(2t+1)) ?

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

What is the first d/(dt)(ln(2t+1)) ?

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

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

\frac{2}{2 t + 1}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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