Understanding Derivatives of Natural Logarithms

The video tutorial explains how to find derivatives involving natural logarithm functions, focusing on the chain rule and properties of logarithms. It provides examples of calculating derivatives for functions like 2ln(x) and ln(4x), demonstrating both the chain rule and an alternative method using logarithm properties. The tutorial emphasizes understanding when to apply the chain rule and how different methods can yield the same result.

What is the derivative of natural log x?

• ln(x)

• x

• x^2

• 1/x

When applying the chain rule to natural log u, what is the derivative formula?

• 1/u

• u'/u

• u

• ln(u)

What is the result of applying the chain rule to ln(x)?

• 1/x

• x

• 0

• ln(x)

In the example f(x) = 2 * ln(x), what is the derivative f'(x)?

• 2/x

• ln(x)/2

• x/2

• 2ln(x)

For the function f(x) = ln(4x), what is the inner function u?

• 4

• ln(x)

• x

• 4x

What is the derivative of ln(4x) using the chain rule?

• 1/x

• 4/x

• x/4

• ln(4x)

How can ln(4x) be rewritten using logarithmic properties?

• ln(4) + ln(x)

• ln(4x^2)

• 4ln(x)

• ln(x/4)

What is the derivative of ln(4) with respect to x?

• 0

• 1

• 4

• ln(x)

Which method is more common for finding the derivative of ln(4x)?

• Using integration

• Using substitution

• Using logarithmic properties

• Using the chain rule

What is the derivative of a constant like ln(4)?

• ln(4)

• 0

• 1

• 4