What is the first d/(dn)(ln(n+1)) ?

The first d/(dn)(ln(n+1)) is 1/(n+1)

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d/(dn)(ln(n+1))

\frac{d}{d n} (ln (n + 1))

\frac{1}{n + 1}

Solution steps

\frac{d}{d n} (ln (n + 1))

Apply the chain rule:

\frac{1}{n + 1} \frac{d}{d n} (n + 1)

= \frac{1}{n + 1} \frac{d}{d n} (n + 1)

\frac{d}{d n} (n + 1) = 1

= \frac{1}{n + 1} \cdot 1

Simplify

= \frac{1}{n + 1}

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