How to use the product rule to take the derivative with trig functions with trig functions

The video tutorial explains the product rule in calculus, demonstrating how to differentiate a product of two functions. It provides a step-by-step application of the rule using specific functions, highlights the importance of correctly handling negative signs, and simplifies the resulting expression. Common mistakes, such as forgetting the negative sign, are also discussed to help students avoid errors.

What is the initial step in applying the product rule to functions F(x) and G(x)?

• Integrate F(x) and G(x)

• Differentiate F(x) and multiply by G(x)

• Add F(x) and G(x)

• Multiply F(x) by G(x)

When calculating H'(x), what is the derivative of G(x) if G(x) is cosine of x?

• Negative cosine of x

• Cosine of x

• Negative sine of x

• Sine of x

What is the derivative of F(x) if F(x) is X^3?

• 3X^2

• 3X

• X^2

• X^3

What is a common mistake students make when simplifying the expression for H'(x)?

• Forgetting to differentiate G(x)

• Forgetting to multiply by F(x)

• Forgetting to add G(x)

• Forgetting the negative sign with cosine

In the expression for H'(x), what should be done with the term X^3?

• Add it to the end

• Ignore it

• Multiply it by F(x)

• Place it in front