I'm working through some actuarial practice and am lost as to what's going on with the differentiation here (it's been a while since I've had calc):
Derive an expression for $\delta_t$ if accumulation is based on:
(a) simple interest at annual rate i, and
(b) compound interest at annual rate i.
I understand the answer to (a), which is $\delta_t$ = $\frac{ A'(t)}{A(t)}$ = $\frac{i}{1+i \cdot t}$.
However, I don't understand their method of getting $\ln(1+i)$ for part (b).
Any help would be much appreciated!
(p.s. this is Example 1.13 p.40 from Broverman's Mathematics of Investment and Credit 5th ed)