A common error with who’s and whose is to confuse one for the other:
Incorrect: She loves an author who’s books have become hard to find.
Correct : She loves an author whose books have become hard to find.
Incorrect: That’s a regular whose who of Fataverse All-Stars if I do say so myself.
Correct : That’s a regular who’s who of Fataverse All-Stars if I do say so myself.
Who’s is a contraction of the pronoun who and the verb is:
Who’s [who is] that man sitting by your wife?
Who’s Who [Who is Who] is the title of several biographical publications.
Note: The phrase “who’s who” is used to mean a collection of people notable in a certain pursuit, for example, “a who’s who of jazz” or “a who’s who of vulgarity masquerading as humor.”
Whose is the possessive form of the pronoun who:
Helen is the woman whose face launched a thousand ships.
I know whose sunglasses these are.
Alone or before a noun, whose is used to introduce a question:
Whose is that car parked in our driveway?
Whose little dog are you?
Whose children were injured in the mudslide?
Whose is used as a relative to introduce a clause:
Troy Landry, a Cajun whose family goes back three generations, is on a mission to hunt down a monstrous alligator.
The family Tineidae includes the clothes moths, whose larvae feed on woolens, furs, and other textiles.
The usual meaning of whose is “of whom” or “belonging to whom.” Because who is a pronoun that applies only to living creatures, a few obstinate grammar sticklers object to the use of whose as the possessive of which as illustrated in these examples:
I can’t recommend The Magnificent Ambersons, the great Orson Welles film whose ending the studio gutted.
In 1986, a flawed reactor design at Chernobyl, Russia caused a leak whose effects are still being felt today.
Because using which to refer to people is nonstandard, critics argue that using whose to refer to inanimate things like film endings and leaks should not be allowed. This is one of those vain arguments that try to force idiom to conform to logic. The previous examples could be recast to conform to the so-called rule:
I can’t recommend The Magnificent Ambersons, the great Orson Welles film of which the studio gutted the ending.
In 1986, a flawed reactor design at Chernobyl, Russia caused a leak of which the effects are still being felt today.
But the changes hardly lead to stylistic improvement.
I’ll let The Chicago Manual of Style have the last word on whose to mean “of which”:
Some writers object to using whose as a replacement for of which, especially when the subject is not human, but the usage is centuries old and widely accepted as preventing unnecessary awkwardness. Compare “the company whose stock rose faster” with “the company the stock of which rose faster.” Either form is acceptable, but the possessive whose lends greater smoothness. –CMOS, 5.61