How to take derivative of a rational function using quotient rule

The video tutorial covers the process of finding derivatives of functions F(x) and G(x), applying the quotient rule, and simplifying the resulting expression. The instructor begins by introducing the functions and their derivatives, then demonstrates the application of the quotient rule. The tutorial concludes with the simplification of the expression and the presentation of the final answer.

What is the derivative of F(x) = x^3 + 2x^2 - 1?

• x^2 + 4x

• 3x^2 + 4x

• 3x^2 + 2x

• x^3 + 2x

What is the derivative of G(x) = x + 5?

• x

• 1

• 5

• 0

In the quotient rule, what operation is performed after multiplying G(x) by F'(x)?

• Addition

• Division

• Subtraction

• Multiplication

What is the result of expanding and simplifying the expression 3x^3 + 4x^2 + 15x^2?

• 3x^3 + 19x^2

• 3x^3 + 4x^2

• 3x^3 + 19x

• 3x^3 + 15x^2

What is the final simplified form of the derivative in the example?

• 2x^3 + 15x^2 + 20x + 1

• x^3 + 17x^2 + 20x + 1

• 2x^3 + 17x^2 + 15x + 1

• 2x^3 + 17x^2 + 20x + 1