Derivative of a recurrence equation

edit

Given:

var('β α γ t R')
c = function('c')
g = function('g')
f = function('f')
λ = function('λ')

suppose I define a function as

def U(l):
    eq = 0
    for i in range(l):
        eq += (β^i)*(((c(t+i)+α*g(t+i))^(1-R))/(1-R))
    return eq

How do I take the first order derivative w.r.t. C_t C_t+1 and so forth?

I tried:

n = 2
L = U(n)
L.derivative(c(t))

without any luck.