On-line Math 21

Inverse Functions

Derivatives of inverse functions; implicit differentiation

Example 2 Use implicit differentiation to find the derivative of

Öx.

Solution

Start off with the ``frontwards'' function, f(x) = x² . Then the square root is the inverse,

f-1(x) = Öx.

Following the method (not just plugging into the formula) we just went through in general,

f-1(x) = y = Öx y2 = x

Differentiating both sides,

y2 = x 2y dy dx = 1, or dy dx = 1 2y = 1 2Öx .

Of course, we knew that already, but this is a new way to approach it.

Copyright (c) 2000 by David L. Johnson.