Differentiate x^(1/x), twice and fast!

TL;DR

This video teaches how to find the second derivative function of X to the 1 of X power.

Transcript

okay in this video I'm gonna show you guys how to find the second derivative function X to the 1 of X power so let's get work first up notice at the base is equal to X right so let's look at XS e to the Ln X power because Kimmy mark whenever I want to work with the exponential each write you want to have base e right here right and then don't forge... Read More

Key Insights

• ☺️ X to the 1 of X can be converted to e to the ln X over X.
• 📏 The derivative of e to the ln X over X can be found using the quotient rule.
• ☺️ The derivative of X to the 1 of X can be found using the product rule.
• 📏 To find the second derivative function, the quotient rule and product rule need to be applied.
• ❓ The final result of the second derivative function involves simplification and expansion.
• ✊ The second derivative function includes terms such as X, Ln X, and X to the 4th power.
• 😑 The second derivative function can be expressed as a fraction with X to the 4th power as the denominator.

Questions & Answers

Q: How do you convert X to the 1 of X power to e to the ln X over X?

To convert X to the 1 of X power to e to the ln X over X, you need to have base e and raise it to the 1 over X power.

Q: What is the first step to finding the second derivative function?

The first step is to differentiate e to the ln X over X using the quotient rule.

Q: How do you differentiate e to the ln X over X using the quotient rule?

To differentiate e to the ln X over X using the quotient rule, you need to square the denominator, multiply it by the derivative of the numerator, and subtract the numerator multiplied by the derivative of the denominator.

Q: What is the second step to finding the second derivative function?

The second step is to differentiate X to the 1 of X using the product rule.

Summary & Key Takeaways

• The video explains how to convert X to the 1 of X power to e to the ln X over X.

• The first step is to differentiate e to the ln X over X using the quotient rule.

• The second step is to differentiate X to the 1 of X using the product rule.