[R] Derivative of a smooth function

[FMH]

Dear All,

I've been searching for appropriate codes to compute the rate of change and the curvature of  nonparametric regression model whish was denoted by a smooth function but unfortunately don't manage to do it. I presume that such characteristics from a smooth curve can be determined by the first and second derivative operators.

The following are the example of fitting a nonparametric regression model via smoothing spline function from the Help file in R.

#######################################################
attach(cars)
plot(speed, dist, main = "data(cars)  &  smoothing splines")
cars.spl <- smooth.spline(speed, dist)
lines(cars.spl, col = "blue")
lines(smooth.spline(speed, dist, df=10), lty=2, col = "red")
legend(5,120,c(paste("default [C.V.] => df =",round(cars.spl$df,1)),"s( * , df = 10)"), col = c("blue","red"), lty = 1:2, bg='bisque')
detach()

#######################################################


Could someone please advice me the appropriate way to determine such derivatives on the curves which were fitted by the function above and would like to thank you in advance.

Cheers
Fir