Do you want to sum rows or do you want a single number?
Here are the ways to produce both:
julia> df = DataFrame(rand(5, 4), :auto)
5×4 DataFrame
Row │ x1 x2 x3 x4
│ Float64 Float64 Float64 Float64
─────┼─────────────────────────────────────────
1 │ 0.428323 0.757593 0.31246 0.640604
2 │ 0.633038 0.169417 0.528082 0.669834
3 │ 0.0376092 0.786284 0.399867 0.720137
4 │ 0.673165 0.66684 0.437688 0.35086
5 │ 0.614091 0.682412 0.511448 0.495272
julia> transform(df, [:x1, :x2, :x3, :x4] => (+) => :sum_of_rows)
5×5 DataFrame
Row │ x1 x2 x3 x4 sum_of_rows
│ Float64 Float64 Float64 Float64 Float64
─────┼──────────────────────────────────────────────────────
1 │ 0.428323 0.757593 0.31246 0.640604 2.13898
2 │ 0.633038 0.169417 0.528082 0.669834 2.00037
3 │ 0.0376092 0.786284 0.399867 0.720137 1.9439
4 │ 0.673165 0.66684 0.437688 0.35086 2.12855
5 │ 0.614091 0.682412 0.511448 0.495272 2.30322
julia> transform(df, [:x1, :x2, :x3, :x4] => ((v...) -> sum(+(v...))) => :total_sum)
5×5 DataFrame
Row │ x1 x2 x3 x4 total_sum
│ Float64 Float64 Float64 Float64 Float64
─────┼────────────────────────────────────────────────────
1 │ 0.428323 0.757593 0.31246 0.640604 10.515
2 │ 0.633038 0.169417 0.528082 0.669834 10.515
3 │ 0.0376092 0.786284 0.399867 0.720137 10.515
4 │ 0.673165 0.66684 0.437688 0.35086 10.515
5 │ 0.614091 0.682412 0.511448 0.495272 10.515
However, since you are struggling maybe using DataFramesMeta.jl will be easier for you:
julia> using DataFramesMeta
julia> @transform(df, :sum_of_rows = :x1 + :x2 + :x3 + :x4)
5×5 DataFrame
Row │ x1 x2 x3 x4 sum_of_rows
│ Float64 Float64 Float64 Float64 Float64
─────┼──────────────────────────────────────────────────────
1 │ 0.428323 0.757593 0.31246 0.640604 2.13898
2 │ 0.633038 0.169417 0.528082 0.669834 2.00037
3 │ 0.0376092 0.786284 0.399867 0.720137 1.9439
4 │ 0.673165 0.66684 0.437688 0.35086 2.12855
5 │ 0.614091 0.682412 0.511448 0.495272 2.30322
julia> @transform(df, :total_sum = sum(:x1 + :x2 + :x3 + :x4))
5×5 DataFrame
Row │ x1 x2 x3 x4 total_sum
│ Float64 Float64 Float64 Float64 Float64
─────┼────────────────────────────────────────────────────
1 │ 0.428323 0.757593 0.31246 0.640604 10.515
2 │ 0.633038 0.169417 0.528082 0.669834 10.515
3 │ 0.0376092 0.786284 0.399867 0.720137 10.515
4 │ 0.673165 0.66684 0.437688 0.35086 10.515
5 │ 0.614091 0.682412 0.511448 0.495272 10.515