# Derivative of root functions

Root functions are differentiated by first converting them to a fractional power. The familiar power derivation rules is then used. The fractional power functions are continuous and their domain is Example 1 Example 2 Example 3

Differentiate the function Note that this is a combined function. We must remember the derivative of the inner function. Note. The domain of the derivative function is the open interval -1 < x < 1

Example 4

Differentiate the function Domain of definition Product rule of derivative Example 5

Find the minimum value of the function in the previous example

The continuous function gets its minimum value at the zero point of the derivative or at the end point of the interval

## Function ## Derivative function Zeros of the derivative function is found by zeros of the numerator The zero point belongs to the function domain. We create a behavior chart of the function Based on the behavior chart, the minimum value is obtained in the zero of the derivative  Turn on the subtitles if needed