The phrase "trace the influence" is correct and usable in written English.
You can use it when discussing the impact or effect that one thing has had on another, often in academic or analytical contexts.
Example: "In her research, she aims to trace the influence of social media on youth culture."
Alternatives: "map the impact" or "follow the effect."
Highlights include rare examples of his early primitivist and surrealist styles, which trace the influence of pre-Columbian art on his work.
Felitti and Robert Anda, of the C.D.C., then designed a study to trace the influence of childhood experiences on adult illness and death.
And it is not difficult to trace the influence of these two men without qualities on the work of Joyce and Musil and Beckett, and on the 20th century's evolution of the antihero.
Collins signalled his ambitions for the book in the preface to the first edition, in which he wrote: "In some of my former novels, the object proposed has been to trace the influence of circumstances upon character.
But the events in this county, population 44,000, also suggest how hard it can be to accurately trace the influence of national debates and moods on individual episodes of antagonism.
Digging more deeply into James's early youth -- in the obscure Irish town of Tinneranny and later in Buffalo -- we more fully comprehended the scars left on his family by the potato famine, and were able to trace the influence of these early fears on his son's life and art.
Rather, the (academic) goal would be to describe the positions of the two theorists, compare them, note their place in the history of political thought, trace the influences that produced them and chart their own influence on subsequent thinkers in the tradition.
In many of them, Quart traces the influence of money-obsession on her own imagination.
And, in a chapter called "Other Bodies in the Swamp," he traces the influence of "Psycho" on more recent movies.
As an example of N.L.F methods of collectivizing & organizing, writer traces the influence the Front had a the village of Ich Thien, from 1963 to 1965.
This looks like a genuinely fascinating exhibition that traces the influence of Carroll on art, from the pre-Raphaelites to today.
