Trigonometric Functions and Derivatives

The video tutorial explains how to find the derivative of the function f(x) = sin^5(x) using the chain rule. It begins by rewriting the function for easier differentiation, identifies the inner and outer functions, and applies the chain rule to find the derivative. The tutorial then simplifies the derivative expression and evaluates it at pi/3 using trigonometric identities from a 30-60-90 triangle. The final result is presented as a simplified fraction.

What is the initial function given in the problem?

• f(x) = cos^5(x)

• f(x) = sin^5(x)

• f(x) = sec^5(x)

• f(x) = tan^5(x)

How is the function rewritten to make differentiation easier?

• As the fifth power of secant x

• As the fifth power of sine x

• As the fifth power of tangent x

• As the fifth power of cosine x

What is the inner function identified for applying the chain rule?

• cosine x

• tangent x

• sine x

• secant x

Which rule is applied along with the chain rule to find the derivative?

• Exponential rule

• Product rule

• Quotient rule

• Power rule

What is the derivative of sine x with respect to x?

• tangent x

• secant x

• cosine x

• sine x

What is the value of cosine(π/3)?

• 1/2

• 0

• 1

• √3/2

What is the value of sine(π/3)?

• √3/2

• 1

• 0

• 1/2

What is the fourth power of √3/2?

• 1/4

• 1/16

• 3/4

• 9/16

What is the final simplified value of f'(π/3)?

• 45/128

• 45/32

• 45/16

• 45/64

What trigonometric identity is used to find cosine(π/3)?

• Sum and difference formulas

• 45-45-90 triangle

• 30-60-90 triangle

• Pythagorean identity