Sum across multiple columns with dplyr

My question involves summing up values across multiple columns of a data frame and creating a new column corresponding to this summation using dplyr. The data entries in the columns are binary(0,1). I am thinking of a row-wise analog of the summarise_each or mutate_each function of dplyr. Below is a minimal example of the data frame:

library(dplyr)
df=data.frame(
  x1=c(1,0,0,NA,0,1,1,NA,0,1),
  x2=c(1,1,NA,1,1,0,NA,NA,0,1),
  x3=c(0,1,0,1,1,0,NA,NA,0,1),
  x4=c(1,0,NA,1,0,0,NA,0,0,1),
  x5=c(1,1,NA,1,1,1,NA,1,0,1))
> df
   x1 x2 x3 x4 x5
1   1  1  0  1  1
2   0  1  1  0  1
3   0 NA  0 NA NA
4  NA  1  1  1  1
5   0  1  1  0  1
6   1  0  0  0  1
7   1 NA NA NA NA
8  NA NA NA  0  1
9   0  0  0  0  0
10  1  1  1  1  1

I could use something like:

df <- df %>% mutate(sumrow= x1 + x2 + x3 + x4 + x5)

but this would involve writing out the names of each of the columns. I have like 50 columns. In addition, the column names change at different iterations of the loop in which I want to implement this operation so I would like to try to avoid having to give any column names.

How can I do that most efficiently? Any assistance would be greatly appreciated.