Difficult# Reverse Engineer Original Function, Given Point and Derivative

APCALC-ZZNEEE

Let $f$ and $g$ be differentiable functions with the following properties:

**I**. $ g(x) \gt 0$ for all $x$

**II**. $f(0)=1$

If $h(x)=f(x)g(x)$ and $h'(x)=f(x)g'(x)$, then $f(x)=$