Applying the chain rule with natural logarithms

This video covers the chain rule in calculus, including its application and practice problems.

What is the initial step in applying the chain rule to find the derivative of a function?

• Identify the outer and inner functions

• Divide the functions

• Multiply the functions directly

• Add the functions together

Why is it beneficial to rewrite the derivative expression in a simpler form?

• To make it more complex

• To avoid dealing with fractions in both the numerator and denominator

• To make it harder to solve

• To increase the number of terms

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

• x

• 1/x

• ln(x)

• x^2

In the final expression for the derivative, what operation is performed on the terms?

• Division

• Multiplication

• Subtraction

• Addition

What is the final expression for the derivative of the given function?

• ln(x) / x

• 1 + x * ln(x)

• x + ln(x)

• 1/x * (1 + ln(x))