Find the derivative using product rule inside quotient

The video tutorial explains the quotient rule for derivatives, demonstrating how to apply it with the product rule. The instructor simplifies the derivative expression, highlighting potential simplifications for multiple choice questions. The tutorial concludes with the final derivative result, emphasizing the integration of product and quotient rules.

What is the first step in applying the quotient rule?

• Multiply the denominator by the derivative of the numerator

• Take the derivative of the denominator

• Square the numerator

• Multiply the numerator by the derivative of the denominator

When using the product rule within the quotient rule, what is the derivative of X times sine of X?

• X times cosine of X

• Cosine of X

• Sine of X

• 1 times sine of X plus X times cosine of X

What happens to the terms X sine of X and negative X sine of X during simplification?

• They are added together

• They cancel each other out

• They remain unchanged

• They are multiplied

Why is it unnecessary to expand the denominator in the final expression?

• It simplifies the expression further

• There is no benefit in expanding it

• It makes the expression more complex

• It changes the value of the expression

What is the final form of the derivative after simplification?

• X squared cosine of X plus sine of X plus X cosine of X all over X plus 1 squared

• X cosine of X plus sine of X all over X squared

• X sine of X plus cosine of X all over X plus 1

• X squared sine of X plus cosine of X all over X plus 1 squared