Derivatives of Logarithmic Functions | Calculus I (15)

Welcome to the fifteenth lecture in our Calculus I series!

In this video, we expand our differentiation toolkit to include logarithmic functions. We start by defining the derivatives for the natural logarithm, ln(x), and general logarithms, log_b(x).

We also discuss the definition of the number e as a limit, which provides the foundational understanding for why the derivative of ln(x) is simply 1/x. We then work through multiple examples applying the chain rule to logarithmic functions. Finally, we introduce the derivative of the inverse tangent function (arctan) and solve an example combining these concepts.

Key Concepts Covered:
The derivative of natural log: d/dx[ln(x)].
The derivative of general logs: d/dx[log_b(x)].
The definition of e as a limit as n approaches infinity.
Applying the chain rule to logarithmic functions.
The derivative of the inverse tangent function (arctan x).

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TIMESTAMPS: 00:00 - Introduction 00:07 - Derivatives of logarithmic functions 01:45 - e as a limit 03:00 - Example 1 03:47 - Example 2 05:09 - Example 3 06:45 - Example 4 08:00 - Example 5 22:30 - Derivative of inverse tangent 22:45 - Example 6