# Derivative of y = 4ln(tanh(x/2)) | Summary and Q&A

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April 28, 2020
by
The Math Sorcerer
Derivative of y = 4ln(tanh(x/2))

## 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

okay so in this problem we have to find the derivative of this function so we're definitely going to have to use the chain rule so as a good first step I'm thinking it might be beneficial to rewrite it as follows this is for natural log tench and this might seem like a small step but I think it does help so the x over two we can write that as one-h... Read More

### 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.