Derivative of y = 4ln(tanh(x/2))  Summary and Q&A
TL;DR
This video explains how to find the derivative of a function using the chain rule and simplifies the final result.
Key Insights
 💁 Rewriting the function in a simpler form can make it easier to find the derivative using the chain rule.
 🧑💻 The derivative of the natural log function is 1 divided by the expression inside the natural log.
 ❎ The derivative of the hyperbolic secant function is the hyperbolic secant squared function.
 📏 The chain rule is used to find the derivative of the function.
 ✖️ Multiplying constants outside the derivative is a straightforward step in finding the derivative.
 😑 Simplifying the final result can lead to a more concise expression.
 😑 Cancelling out common terms can simplify the final expression further.
Transcript
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Questions & Answers
Q: What is the initial step taken to solve the problem?
The initial step is to rewrite the function in a simplified form by expressing "x/2" as "1/2x".
Q: How is the derivative of the natural log function calculated?
The derivative of the natural log function is calculated as 1 divided by the expression inside the natural log.
Q: What is the derivative of the hyperbolic secant function?
The derivative of the hyperbolic secant function is the hyperbolic secant squared function.
Q: How can the final result be further simplified?
The final result can be simplified by expressing the hyperbolic secant function as 1 divided by the hyperbolic cosine function, and the hyperbolic cosecant function as 1 divided by the hyperbolic sine function.
Summary & Key Takeaways

The problem requires finding the derivative of a function using the chain rule.

The function is rewritten to make it easier to take the derivative.

The derivative is calculated using the chain rule and simplifications are made.