I only see a 3rd derivative here. 1st: labor productivity, 2nd: rate of labor productivity growth, 3rd: acceleration of a rate of labor productivity growth.
The quote in Russian also describes a 3rd derivative.
Let’s say “labor” refers to building houses, and “labor productivity” refers to how many houses are build in a year. This is the first rate of change (1st derivative). For example, “in 2019 one house was built, in 2020 one house was built, in 2021 one house was built”, and the 1st derivative is 1 house per year.
“Labor productivity growth rate” is how much the first rate of change changes (2nd derivative): for example, “in 2019 one house was built, in 2020 two houses were built, in 2021 three houses were built”, the second derivative is 1 house per year per year. This is the second rate of change in that statement.
Finally, “acceleration of labor productivity growth rate” describes how the growth changes (the third rate of change): “in 2019 one house was built, in 2020 two houses were built, in 2021 four houses were built”. The 3rd derivative is 1 house per year per year per year. No other rates of change are mentioned in your statement.
I don't know Russian, but I'd read the English quote as referring to a third derivative - the units of "labour productivity" are work/time; so growth of that is a second derivative. Also if someone said "acceleration of speed" I would assume they meant acceleration, so that only adds one derivative.
Not found in English, but in original Russian - "ускорение темпов роста производительности труда" - about 4,090 results in Google.
"The acceleration of labor productivity growth" in English - about 11,700 results. But that's only a 5th derivative.