Notebook Check: Derivatives Review

What is the derivative of a constant?

• x
• 1
• 0
• π

What is the derivative of x^2?

• 2x

• x

• 4x

• 2

What is the derivative of e^x?

• e^x

• x*e^x

• 1

• e^(x+1)

What is the chain rule used for?

• Calculating integrals
• Graphing functions
• To differentiate functions with multiple terms raised to a power (not equal to 1)

• Solving linear equations

What is the chain rule?

• The chain rule states that the derivative of f(g(x)) is f'(g(x)) + g'(x)
• The chain rule states that if y=[f(x)]n then dy/dx=n [f(x)]n-1f'(x)

• The chain rule states that the derivative of f(g(x)) is f'(g(x)) / g'(x)
• The chain rule states that the derivative of f(g(x)) is f'(g(x)) - g'(x)

What is the product rule?

• The product rule states that (f * g)' = f' * g + f * g'
• The product rule states that (f - g)' = f' - g'
• The product rule states that (f + g)' = f' + g'
• The product rule states that (f / g)' = f' / g + f / g'

What is the product rule used for?

• Solving linear equations
• Calculating integrals
• Graphing functions
• The product rule is used to differentiate a product

What is the power rule for differentiation?

• The power rule states that the derivative of x^n is nx^(n-1)

• The power rule states that the derivative of x^n is n/x^(n+1)

• The power rule states that the derivative of x^n is x^(n/2)

• The power rule states that the derivative of x^n is 2n

What is the quotient rule?

• The quotient rule is (f(x)*g'(x) - g(x)*f'(x)) / (g(x))^2.
• The quotient rule is (f(x)*g'(x) + g(x)*f'(x)) / (g(x))^2.
• The quotient rule is (g(x)*f'(x) - f(x)*g'(x)) / (g(x))^2.
• The quotient rule is (f(x)*g'(x) - g(x)*f'(x)) / (f(x))^2.

What is the quotient rule used for?

• Calculating the area of a circle
• Solving linear equations
• Quotient rule is used to differentiate a quotient

• Finding the integral of a function