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.