get a derivative by knowing two numeric vectors

Question

I know two vectors x and y, how can I calculate derivatives of y with respect to x in R ?

x<-rnorm(1000)
y<-x^2+x

I want to caculate derivative of y with respect to x: dy/dx; suppose I don't know the underlying function between x and y. There can be a value in derivative scale corresponding to each x.

Answer 1

To find the derivative use the numeric approximation: (y2-y1)/(x2-x1) or dy/dx. In R use the diff function to calculate the difference between 2 consecutive points:

x<-rnorm(100)
y<-x^2+x

#find the average x between 2 points
avex<-x[-1]-diff(x)/2
#find the numerical approximation
#delta-y/delta-x
dydx<-diff(y)/diff(x)

#plot numeric approxiamtion
plot(x=avex, dydx)
#plot analytical answer
lines(x=avex, y=2*avex+1)