Find the derivative using quotient rule inside of the product rule

The video tutorial explains the process of finding derivatives using the product and quotient rules. It begins with an introduction to the product rule and its notation, followed by a detailed explanation of finding F prime using the quotient rule. The tutorial then simplifies the expression for F prime and calculates G prime, emphasizing the importance of using brackets. Finally, it combines F prime and G prime to find H prime and concludes with the final simplification steps, including finding common denominators.

What is the product rule used for in calculus?

• To find the derivative of a sum of functions

• To find the limit of a function

• To find the derivative of a product of two functions

• To find the integral of a function

When applying the quotient rule, what is the first step?

• Multiply the numerator by the denominator

• Differentiate the numerator and denominator separately

• Square the denominator

• Add the numerator and denominator

Why is it important to use brackets in the quotient rule?

• To simplify the equation

• To avoid subtracting only part of the numerator

• To make the equation look neat

• To ensure the correct order of operations

What is the derivative of a constant function?

• The constant itself

• The variable

• Zero

• One

What is the result of distributing a negative sign across a bracketed expression?

• The expression remains unchanged

• The expression is multiplied by zero

• Only the first term is negated

• Each term inside the brackets is negated

In the final simplification, what is the common denominator used?

• X squared

• X + 4

• X + 3

• X + 3 squared

What is the derivative of 2x with respect to x?

• 2

• x

• 1

• 0