Part 3/5:
This logarithmic approach is used to maintain the integrity of the derivative since logarithms are not defined for non-positive numbers. Graphing the logarithmic function reveals that values must be greater than zero to calculate ( \ln |X| ), indicating (X) cannot reach zero within this framework, thus providing significant boundaries for the power rule.
Behavior of Functions at Zero
The behavior of functions and their derivatives as they approach zero involves a unique consideration. It is essential to understand that while typical logarithmic functions cannot include zero, the absolute value of logarithmic output can still yield valid results under certain transformations.