Find the double derivative of the natural logarithm

The video tutorial covers the chain rule in calculus, focusing on identifying inside and outside functions. It demonstrates the process of finding the first derivative using the chain rule and then extends to finding the second derivative by applying the quotient and product rules. The tutorial uses logarithmic functions as examples to illustrate these concepts.

What is the first step in applying the chain rule?

• Multiply the derivatives

• Differentiate the inside function

• Identify the outside function

• Add the derivatives

In the context of the chain rule, what is the role of the inside function?

• It is the function to be differentiated first

• It is the function that is ignored

• It is the function that remains unchanged

• It is the function that is differentiated last

When finding the first derivative using the chain rule, what do you do after differentiating the outside function?

• Divide by the derivative of the inside function

• Add the derivative of the inside function

• Multiply by the derivative of the inside function

• Subtract the derivative of the inside function

What mathematical rule is used within the quotient rule to find the second derivative?

• Chain rule

• Difference rule

• Product rule

• Sum rule

What happens to the derivative of the numerator when applying the quotient rule for the second derivative?

• It is squared

• It is ignored

• It doubles

• It becomes zero