deriv function

Differentiation of mvp objects

## S3 method for class 'mvp'
deriv(expr, v, ...)
## S3 method for class 'mvp'
aderiv(expr, ...)

Arguments

• expr: Object of class mvp
• v: Character vector. Elements denote variables to differentiate with respect to
• ...: Further arguments. In deriv(), a non-negative integer argument specifies the order of the differential, and in aderiv() the argument names specify the differentials and their values their respective orders

Author(s)

Robin K. S. Hankin

See Also

taylor

Details

deriv(S,v) returns $d^rS/dv1...dvr$. Here, v

is a (character) vector of symbols.

deriv(S,v,n) returns the n-th derivative of S with respect to symbol v, $d^nS/dv^n$.

aderiv() uses the ellipsis construction with the names of the argument being the variable to be differentiated with respect to. Thus aderiv(S,x=1,y=2) returns $d^3S/dxdy^2$.

Examples

(p <- rmvp(10,4,15,5))
deriv(p,"a")
deriv(p,"a",3)
deriv(p,letters[1:3])
deriv(p,rev(letters[1:3]))  # should be the same

aderiv(p,a=1,b=2,c=1)

## verify the chain rule:
x <- rmvp(7,symbols=6)
v <- allvars(x)[1]
s <- as.mvp("1  +  y  -  y^2 zz  +  y^3 z^2")
LHS <- subsmvp(deriv(x,v)*deriv(s,"y"),v,s)   # dx/ds*ds/dy
RHS <- deriv(subsmvp(x,v,s),"y")              # dx/dy

LHS - RHS # should be zero