Your question is very broad. There are many ways to do this, even without assuming a specific function. For the following I assume that you have a good reason to use the Gompertz model.
First let's fit the model:
y <- c(0.5,3.0,22.2,46.0,77.3,97.0,98.9,100.0)
x <- seq_along(y)
fit <- nls(y ~ SSgompertz(x, Asym, b2, b3), data = data.frame(x, y))
curve(predict(fit, newdata = data.frame(x)), add = TRUE)
Now, in order to get the desired slopes, you'll need to calculate the first derivative of the fitted function. That is simple highschool maths. In fact, it's so simple that even R can do it although it is not a computer algebra system.
#assign coefficients into global environment
#create function that returns the gradient
dGomp <- deriv((y ~ Asym*exp(-b2*b3^x)), "x", func = TRUE)
#the model slopes:
## 0.1010109 6.9594864 27.3791349 31.0194397 20.4539646 10.6588397 5.0141801 2.2561393