Barrons AP Calculus

Derivative  of  inverse function

Simply put, the derivative of the inverse of a function at a point is the
reciprocal of the derivative of the function at the corresponding point.

Figure  N3–8

Example 33 __

If f (3) = 8 and f ′(3) = 5, what do we know about f −^1?

SOLUTION: Since f passes through the point (3,8), f −^1 must pass through the
point (8,3). Furthermore, since the graph of f has slope 5 at (3,8), the graph of f

− (^1) must have slope at (8,3).

Example 34 __

A function f and its derivative take on the values shown in the table. If g is the
inverse of f, find g′(6).