Trigonometric Derivatives and Values

The video tutorial explains how to differentiate a function f(x) = x * cos(x) * sin(x) using the product rule. It covers the application of the product rule to a product of three functions, simplifying the derivative, and calculating specific values of the derivative at x = 2 and x = π/2. The tutorial also includes a review of trigonometric values using the unit circle.

What is the main challenge in finding the derivative of the function f(x) = x * cos(x) * sin(x)?

• The function is a quotient of three functions.

• The function is a product of three functions.

• The function is a power of three functions.

• The function is a sum of three functions.

When applying the product rule to f(x) = x * cos(x) * sin(x), what is chosen as the first function?

• x * cos(x)

• x

• sin(x)

• cos(x)

In the process of differentiation, what rule is applied to find the derivative of cos(x) * sin(x)?

• Product Rule

• Power Rule

• Chain Rule

• Quotient Rule

What is the derivative of x with respect to x?

• 0

• 1

• x

• 2x

What is the derivative of sin(x) with respect to x?

• cos(x)

• -sin(x)

• -cos(x)

• sin(x)

What mode should the calculator be in to evaluate trigonometric functions for f'(2)?

• Radian mode

• Graphing mode

• Degree mode

• Scientific mode

What is the approximate value of f'(2) rounded to four decimal places?

• -1.6857

• 1.6857

• -0.6857

• 0.6857

What is the value of cos(π/2)?

• -1

• 1

• 0

• π/2

What is the value of sin(π/2)?

• π/2

• 0

• 1

• -1

What is the exact value of f'(π/2)?

• -π/2

• 1

• π/2

• 0