I guess we're really talking about the first derivative of PRODUCTIVITY_GROWTH in the formula GDP/CAP(t) = GDP/CAP(t-1) * (1 + PRODUCTIVITY_GROWTH(t)).
That graph on my comment is the rate of change of productivity (on a relative base, so it's not a derivative, a derivative would be a small bit biased lower). It's what you are calling PRODUCTIVITY_GROWTH. (I didn't find one with the raw productivity.)
You can see directly on the graph that it stays for some times dancing around 0. Most of the times it's higher, but the times with a near 0 average are quite long. If you "integrate" it over the exponentials, you will get some times of approximately linear growth, separated by times of almost no growth. Those times of almost no growth are what people normally talk about when they talk about productivity stagnation. One of those was at the 80s when the computers were taking over offices, another one is quite recent, after the 2008 crisis.
Anyway, the GDP per capita graph is very different.
But, anyway, that's GDP per capita. Data for productivity is much less available, but here is some for the US alone (that's the change annualized):
https://fred.stlouisfed.org/graph/?id=PRS85006092,
Notice that the rate of change itself (first derivative) stays for ages around 0.