Survival of the fittest was actually coined by an economist, Herbert Spencer after reading Darwin's 1859 publishing of On the Origin of Species by Means of Natural Selection, or the Preservation of Favoured Races in the Struggle for Life.
A most notable influence was on that of Sigmund Freud. Freud had all of Darwin's books and even large portions of his contribution to psychology can have the threads of Darwinian theories.
Although Darwin never coined the term "survival of the fittest," the impact of his research and writing have obvious influence in the notion that all species moved forward on the backs of the "fittest." In other words, through natural selection our ancestors have passed forward the more favorable genes/traits for us to live successfully.
These ideas will change, look for a new book coming out in the next 3-5 years. ~RPA