Part 2/5:
This formula is simple and applies to the natural logarithm of positive numbers only, making it limited when considering negative values or scenarios where ( x ) might approach zero.
Challenges with Negative Values
When examining functions like ( y = x^{1.3} ), one can quickly run into issues when substituting negative values. For instance, if ( x = -1 ) is input into the function, it leads to ( \ln(-1^{1.3}) ), which becomes undefined in the realm of real numbers. Consequently, one cannot straightforwardly apply ordinary logarithmic differentiation methods in these cases.