Derivatives of Composites and the Chain Rule

What is the date and time of the upcoming test mentioned in the introduction?

• May 20th at 4:00 p.m. Eastern

• May 10th at 1:00 p.m. Eastern

• May 12th at 2:00 p.m. Eastern

• May 15th at 3:00 p.m. Eastern

What is the derivative of the product of two functions f(x) and g(x)?

• f(x) + g(x)

• f(x) * g(x)

• f'(x) * g(x) + f(x) * g'(x

• f'(x) * g'(x)

Which rule is used to find the derivative of a composite function?

• Product Rule

• Power Rule

• Quotient Rule

• Chain Rule

What is the derivative of x^2 - 3xy + 4y^5 with respect to x?

• 2x - 3(y + x * dy/dx) + 20y^4 * dy/dx

• 2x - 3(dy/dx) + 20y^4

• 2x - 3y + 20y^4 * dy/dx

• 2x - 3y + 20y^4

Given that db/dt = 6 * sqrt(10 - b), what is the second derivative d^2b/dt^2?

• -36

• -18

• 18

• 36

If f(2) = 7 and f'(2) = 5, what is the slope of the inverse function at x = 7?

• 5

• 1/7

• 7

• 1/5

What is the value of G'(-1) given the table values?

• -12

• 12

• -3

• 3

What is the slope of the tangent line to the function H(x) at x = 2?

• -2/3

• 1

• 2/3

• -1

Given K(x) = G(x) / (G(x) + 2), what is K'(3) if G(3) = 4 and G'(3) = 4?

• 4/9

• 2/3

• 4/3

• 2/9

What is the correct approach to solve for the derivative of a function involving a quotient?

• Use the product rule

• Use the chain rule

• Use the quotient rule

• Use the power rule