Take the derivative using the product rule and chain rule

The video tutorial explains how to find the derivatives of two functions, H(x) and G(x), using the product and chain rules. It begins by introducing the functions and then demonstrates the step-by-step process of calculating their derivatives. The tutorial emphasizes the application of the product rule to combine the derivatives, providing a comprehensive understanding of the process.

What is the derivative of the function H(x) = (2x - 1)^2?

• 8x - 4

• 4x - 2

• 2x - 1

• 4x + 2

Which rule is primarily used to find the derivative of G(x) = cosecant(2x)?

• Product Rule

• Chain Rule

• Power Rule

• Quotient Rule

What is the simplified form of the derivative G'(x) for G(x) = cosecant(2x)?

• -2 cosecant(2x) cotangent(2x)

• 2 cosecant(2x) cotangent(2x)

• -cosecant(2x) cotangent(2x)

• cosecant(2x) cotangent(2x)

When combining the derivatives of H(x) and G(x), which rule is applied?

• Chain Rule

• Product Rule

• Quotient Rule

• Sum Rule

What is the final expression for the derivative when applying the product rule to H(x) and G(x)?

• 8x - 4 cosecant(2x) + 2 cosecant(2x) cotangent(2x)

• 8x - 4 + 2 cosecant(2x)

• 8x - 4 cosecant(2x) - 2 cosecant(2x) cotangent(2x)

• 8x - 4 cosecant(2x) + 2x - 1