Derivatives of inverse functions including inverse trig.

Problem

Let f and g be inverse functions.
The following table lists a few values of f, g, and g, prime.
xf, left parenthesis, x, right parenthesisg, left parenthesis, x, right parenthesisg, prime, left parenthesis, x, right parenthesis
minus, 354minus, start fraction, 1, divided by, 4, end fraction
4minus, 322
f, prime, left parenthesis, 4, right parenthesis, equals
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, p, i or 2, slash, 3, space, p, i