The derivative of f(t * a + c)
wrt t
at 0 is the Jacobian vector product J(f, c) * a
.
julia> using ForwardDiff
julia> foo(x) = [x[1], x[1]*x[3], x[2]^2]
foo (generic function with 1 method)
julia> ForwardDiff.derivative(t->foo([1,2,3] * t + [3, 4, 5]), 0)
3-element Vector{Int64}:
1
14
16
julia> ForwardDiff.jacobian(foo, [3,4,5]) * [1,2,3]
3-element Vector{Int64}:
1
14
16