Understanding Derivatives of Logarithmic Functions

This video tutorial provides additional examples of determining derivatives involving logarithmic functions with bases other than e. It begins with a brief overview of the derivative formulas for basic and composite log functions, emphasizing the use of the chain rule. The video then presents two examples: the first involves a log base 5 function, and the second involves a log base 2 function with a composite function, requiring the chain rule. The tutorial concludes with a preview of the next video, which will cover derivatives involving a product of exponential and log functions.

What is the derivative of log base 'a' of x with respect to x?

• Natural log of a divided by x

• Natural log of x divided by a

• x divided by natural log of a

• 1 divided by x times natural log of a

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CCSS.HSF-IF.C.8B

When do we need to apply the chain rule in finding derivatives of log functions?

• When the function is linear

• When the base is e

• When the function is composite

• When the base is 10

In the first example, what is the base of the logarithm?

• 2

• e

• 5

• 10

Why is the chain rule not applied in the first example?

• Because the derivative is zero

• Because the function is not composite

• Because the base is 5

• Because the base is e

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CCSS.HSA.APR.C.4

In the second example, what is the expression for U?

• x to the 4th + 3x

• x squared + 3

• 4x cubed + 3

• x to the 5th + 2x

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CCSS.HSA.APR.C.4

What is the derivative of U in the second example?

• x to the 4th + 3

• 4x cubed + 3

• 2x + 3

• 3x squared + 4

What is the base of the logarithm in the second example?

• 10

• e

• 5

• 2

What is the denominator in the final expression for the derivative in the second example?

• 4x cubed + 3

• x to the 4th + 3x times natural log 2

• x squared times natural log 2

• Natural log 2

What will the next video focus on?

• Derivatives of trigonometric functions

• Applications of derivatives

• Integration of log functions

• Derivatives of exponential and log function products

What is the purpose of the current video?

• To introduce new derivative formulas

• To provide additional examples of log derivatives

• To explain the history of logarithms

• To solve complex integrals