Understanding Derivatives and Rules

The video tutorial explains how to find the derivative of a function using the product and chain rules. It begins by identifying the inner functions and then applies the rules to calculate the derivative. The process involves substitution and simplification of the derivative expression, followed by factoring to achieve a simplified form. The tutorial concludes with a discussion on the necessity of algebraic simplification.

What is the main challenge in finding the derivative of the given function?

• The function is a simple polynomial.

• The function is a constant.

• The function is a product of two composite functions.

• The function involves trigonometric identities.

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CCSS.HSF-BF.A.1C

What is the inner function U in the first composite function?

• 3X to the 5th + 1

• 5X to the 3rd + 2

• 2X to the 7th - 5

• X squared

What is the derivative of the inner function V?

• 10X to the 5th

• 14X to the 6th

• 7X to the 2nd

• 15X to the 4th

Which rule is applied first when finding the derivative of the product of two functions?

• Quotient Rule

• Chain Rule

• Product Rule

• Power Rule

What is the derivative of U to the 4th with respect to X?

• 5U to the 4th x U'

• 3U to the 2nd x U'

• 2U to the 1st x U'

• 4U to the 3rd x U'

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CCSS.HSA.APR.C.4

What is the first step in simplifying the derivative expression?

• Adding like terms

• Factoring out common terms

• Dividing by a constant

• Multiplying all terms

What is the greatest common factor of 126X to the 6th and 60X to the 4th?

• 18X to the 3rd

• 12X to the 2nd

• 24X to the 5th

• 6X to the 4th

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CCSS.HSA.APR.B.2

How many factors of 3X to the 5th + 1 are factored out?

• 2

• 3

• 4

• 5

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CCSS.HSA.APR.C.4

What is the final expression for the derivative in its factored form?

• 5X to the 3rd x 4X to the 6th + 2X to the 7th - 5 to the 9th

• 6X to the 4th x 3X to the 5th + 1 to the 3rd x 2X to the 7th - 5 to the 8th

• 8X to the 6th x 5X to the 7th + 1 to the 2nd

• 7X to the 5th x 2X to the 8th + 3X to the 4th - 1

What is the purpose of simplifying the derivative expression?

• To change the original function

• To make it more complex

• To make it easier to understand and use

• To increase the number of terms