Understanding Derivatives of Polynomial Functions

This video tutorial covers the process of finding derivatives of polynomial functions. It begins with an introduction to the power and constant rules for derivatives. The tutorial provides examples of calculating derivatives for various polynomial expressions, including using the distributive property and the chain rule. It emphasizes the importance of simplifying expressions before derivation and demonstrates these techniques through step-by-step examples.

What is the derivative of a constant term in a polynomial?

• The constant times x

• The constant itself

• 0

• 1

What is the derivative of x^3 using the power rule?

• x^3

• x^2

• 3x^3

• 3x^2

Using the power rule, what is the derivative of x^5?

• 5x^4

• 5x^5

• x^4

• 4x^5

What is the derivative of 4x^5?

• 20x^4

• 5x^4

• 4x^4

• 20x^5

When distributing 7x to (2x - x^3), what is the resulting expression?

• 14x^2 - 7x^4

• 14x^3 + 7x^4

• 14x^3 - 7x^3

• 14x^2 + 7x^4

What is the result of differentiating 14x^2?

• 14x

• 28x

• 28x^2

• 14x^2

What is the derivative of 3x + 2 when expanded and differentiated?

• 9x + 4

• 18x + 12

• 12x + 6

• 6x + 4

What is the derivative of a squared binomial like (3x + 2)^2?

• 18x + 12

• 12x + 6

• 9x^2 + 12x + 4

• 6x + 4

How do you simplify a polynomial division before finding its derivative?

• Divide each term by the monomial

• Add the exponents of like terms

• Subtract the exponents of like terms

• Multiply each term by the divisor

What is the derivative of 4x^3 after simplifying the division?

• 4x^2

• 12x^2

• 12x^3

• 4x^3