Derivatives and Taylor series in Julia using ForwardDiff.jl

derivatives.jl

using FowardDiff

# Derivative of f
D(f) = x -> FowardDiff.derivative(f, x)

# nth Derivative of f
D(f, n) = let
  F = f
  while n > 0
    F = D(F)
    n -= 1
  end
  F
end

# Taylor Series approximation of f at x0 with n terms
T(f, x0, N) = x -> sum([D(f, n)(x0) * (x - x0)^n / factorial(n) for n ∈ 0:N])