Part 1/5:
Understanding Derivatives of Logarithmic Functions
In mathematics, derivatives provide insight into how functions behave, particularly concerning their rates of change. In this article, we will explore the derivatives of logarithmic functions, specifically the bases of logarithms including ( \log_a(x) ) and ( \ln(x) ) (the natural logarithm). We will achieve this through implicit differentiation and the chain rule, which are foundational techniques in calculus that simplify the process of finding derivatives.