Calculus Derivatives and Rules

The video tutorial explains how to find the derivatives of two functions, g(x) and h(x), using the product and quotient rules of differentiation. Given specific values for f(pi/4) and f'(pi/4), the tutorial walks through the steps to calculate g'(pi/4) and h'(pi/4). The product rule is applied to g(x) = f(x) * sin(x), and the quotient rule is applied to h(x) = f(x) / cos(x). The tutorial provides detailed calculations and simplifications to arrive at the final results for g'(pi/4) and h'(pi/4).

What is the value of f(π/4) given in the problem?

• 12

• 9

• 6

• 3

Which rule is used to find the derivative of a product of two functions?

• Chain Rule

• Sum Rule

• Quotient Rule

• Product Rule

What is the derivative of sin(x)?

• -sin(x)

• -cos(x)

• cos(x)

• tan(x)

What is the value of g'(π/4) after simplification?

• 6√2/2

• 9√2/2

• 12√2/2

• 3√2/2

Which rule is used to find the derivative of a quotient of two functions?

• Chain Rule

• Power Rule

• Product Rule

• Quotient Rule

What is the derivative of cos(x)?

• -cos(x)

• cos(x)

• -sin(x)

• sin(x)

What is the expression for the denominator in the quotient rule?

• Original denominator

• Original numerator

• Square of the numerator

• Square of the denominator

What is the value of h'(π/4) after simplification?

• 9√2

• 6√2

• 3√2

• 12√2

What is the reciprocal of 1/2?

• 1/2

• 4

• 1

• 2

What operation is performed after finding the derivative using the quotient rule?

• Division

• Addition

• Subtraction

• Multiplication by reciprocal