It has been some 30 years since I took calculus, and so my recollection of the derivative rules is a bit fuzzy.
Let $f(h)$ be a function:
$f(h) = ln(1 + ha_1) + ln(1 + ha_2) + ... + ln(1 + ha_n)$
where $a_1, a_2, ..., a_n$ are constants.
Then the second derivative of $f(h)$ with respect to $h$ is
$\frac{d^2 f}{dh^2} = -\sum_{i=1}^{N} \frac{a_i^2}{(1 + ha_i)^2}$
Does this look right? Thanks.