Apply the product rule of taking the derivative with sine

The video tutorial explains how to identify and label two functions, find their derivatives, and apply the product rule to solve a problem. The instructor uses F of X and G of X as labels and demonstrates the process of finding derivatives and applying the product rule step-by-step. The tutorial emphasizes the importance of writing expressions correctly and provides tips for simplifying calculations.

What are the two functions identified in the product?

• F(x) = 2x and G(x) = tan(x)

• F(x) = x^2 and G(x) = sin(x)

• F(x) = 2x and G(x) = sin(x)

• F(x) = 2x and G(x) = cos(x)

What is the derivative of F(x) = 2x?

• 2

• x

• sin(x)

• cos(x)

What is the derivative of G(x) = sin(x)?

• cos(x)

• 2

• sin(x)

• x

Which rule is applied to combine the derivatives and original functions?

• Product Rule

• Chain Rule

• Quotient Rule

• Sum Rule

In the final expression, what should be written in front of cos(x) to save time?

• x^2

• sin(x)

• 2x

• 2