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.

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

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.

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.