differentiating a numeric vector
What functions exist for differentiating a numeric vector (in my case spectral data)? That is, experimental data without an analytical function. ie,
x <- seq(1,10,0.1) y=x^3+rnorm(length(x),sd=0.01) #although the real function would be nothing simple like x^3... derivy <- ....
I know I could just use diff(y) but it would be nice to estimate derivatives at the endpoints, calculate higher-order derivatives, and maybe have some smoothing options ie by differentiating a spline or something like that.