On-line Math 21

2.2  Differentiation Rules

Example 6 Find

æ è Ö   x2+x   ö ø ¢.

Solution

For this function, clearly the square root is the ``outside'' function. That is, the composition is to first take x and compute x²+x , then take the square root. So, since the chain rule tells you to work from the outside in, first differentiate the square root. The derivative of

Öu

is

d du Öu = 1 2Öu ,

so

æ è Ö   x2+x   ö ø ¢ = 1 2 Ö x2+x (2x+1).

Copyright (c) 2000 by David L. Johnson.