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, highlighting the importance of correctly handling negative signs. The tutorial emphasizes common mistakes students make, such as forgetting the negative sign in trigonometric functions, and offers tips for simplifying expressions.

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

• Add the functions together

• Multiply the derivatives of the functions

• Subtract the functions

• Find the derivative of each function separately

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

• Negative cosine of x

• Sine of x

• Negative sine of x

• Cosine of x

In the expression for H'(x), what is the role of the term 3x^2?

• It is the derivative of F(x)

• It is a constant multiplier

• It is the original function F(x)

• It is the derivative of G(x)

Why is it important to remember the negative sign in the derivative of cosine?

• It simplifies the calculation

• It changes the function to a positive sine

• It affects the final sign of the derivative

• It is a common mistake that leads to incorrect results

What should be done with the term x^3 in the final expression of H'(x)?

• It should be placed in front of the expression

• It should be ignored

• It should be multiplied by the derivative

• It should be added to the derivative