In “Instrumental Flying“, we defined as the inverse of and repectively.
To find the derivative of , let
By (see Exercise-1) and (see Exrecise-2),
Similarly, to find let
By and ,
, since (see Exercise-3).
Exercise-1 Show that .
Exercise-2 Show that .
Exercise-3 Show that
Exercise-4 Differentiate directly (hint: see”Deriving Two Inverse Functions“).