Calculating Derivatives Numerically

• Simple:
  [; f'(x) = \lim_{ \varepsilon \rightarrow 0 } \frac{f(x+\varepsilon)-f(x)}{\varepsilon} ;]
• Better:
  [; f'(x) = \lim_{ \varepsilon \rightarrow 0 } \frac{f(x+\varepsilon)-f(x-\varepsilon)}{2\varepsilon} ;]
• Cost: 2 Function Evaluations

def df(f,x,eps=1.0E-3):
    return ( f(x+eps)-f(x-eps) )/(2.0*eps)


def d2f(f,x,eps=1.0E-3):
    return ( df(f,x+eps,eps)-f(f,x-eps,eps) )/(2.0*eps)