For example, I have the following function

```
function test_fun(state)
x, y = state # 2 values
[x*y^2]
end
state = [2,3]
test_fun(state)
```

I’d like to find the mixed derivative \frac{d^2f}{dxdy} for vector case.

I can accompish this with the code below

```
jac₁ = x -> ForwardDiff.jacobian(test_fun, x)
jac₁(state) # [9 12]
jac₂ = x -> ForwardDiff.jacobian(jac₁, x)
jac₂(state) # [[0; 6], [6, 4]]
out = jac₂(state)[1,2] # 6
```

but this requires all matrix elements to be computed.

If I try to reduce this procedure as follows

```
jac₁ = x -> ForwardDiff.jacobian(test_fun, x[1]) # df/dx derivative
println(jac_test_(state))
```

The error emerges:

```
MethodError: no method matching jacobian(::typeof(test_fun), ::Int64)
```