# Derivative of a recurrence equation

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.