Understanding Derivatives of Composite Functions

The video tutorial explains how to determine the derivative of a function involving a natural logarithm. It begins with an introduction to the problem and the derivative form, followed by an explanation of composite functions. The tutorial then provides a detailed calculation of the derivative, emphasizing the importance of correctly applying logarithmic properties. The video concludes with a caution against misapplying these properties and hints at further examples in the next video.

What is the inner function u in the given composite function?

• x squared plus 4x

• x squared minus 4x

• x plus 4

• x minus 4

What is the derivative of the inner function u, denoted as u prime?

• x squared plus 4

• 2x plus 4

• 2x minus 4

• x squared minus 4

How is the derivative of the natural log of a function expressed?

• u squared minus u prime

• u prime divided by u

• u times u prime

• 1/u times u prime

What is the factored form of the derivative's numerator?

• x times (x plus 4)

• x times (x minus 4)

• 2 times (x minus 2)

• 2 times (x plus 2)

Which property of logarithms is incorrectly applied to the given function?

• Logarithm of a product

• Logarithm of a quotient

• Logarithm of a power

• Logarithm of a sum

Why can't the function be rewritten as the difference of two logs?

• Because it is a sum

• Because it is a product

• Because it is not a quotient

• Because it is a power