Most library functions won't be defined in assembly language, at least not in the sense of the addition operator directly mapping to the ADD
instruction. If you want to re-write the library in assembly, you'll have to implement the function using whatever capabilities that your processor has available. Most library functions will require a separate assembly language subroutine, not just a single operation. The easiest way to approach this is to get the individual library subroutines working in isolation, then incorporate them into the larger program.
You can compile the C code and examine the disassembled output, but beware of compiler optimizations that can make the output hard for a human to follow.
May I ask what the purpose is behind this task? Since a compiler is essentially a C to assembly-language translator, there's rarely a need to do this by hand. Is this homework?