Differentiation Rules and Applications

The video tutorial explains how to differentiate functions using the product, quotient, and chain rules. It starts with the product rule, showing how to find the derivative of a product of two functions. Next, it covers the quotient rule, detailing the process for differentiating a function that is a quotient of two other functions. Finally, the chain rule is introduced for differentiating composite functions. Each section uses a table of function values to calculate specific derivatives, providing a practical application of these differentiation techniques.

What is the product rule used for in differentiation?

• Finding the derivative of a sum of two functions

• Finding the derivative of a product of two functions

• Finding the derivative of a quotient of two functions

• Finding the derivative of a composite function

If h(x) = f(x) * g(x), what is the expression for h'(x) using the product rule?

• f(x) * g(x)

• f'(x) * g'(x)

• f'(x) * g(x) - g'(x) * f(x)

• f(x) * g'(x) + g(x) * f'(x)

What is the value of h'(4) if f(4) = 2, g'(4) = 2, g(4) = 1, and f'(4) = 3?

• 8

• 7

• 6

• 5

What is the quotient rule used for in differentiation?

• Finding the derivative of a sum of two functions

• Finding the derivative of a product of two functions

• Finding the derivative of a composite function

• Finding the derivative of a quotient of two functions

If h(x) = f(x) / g(x), what is the expression for h'(x) using the quotient rule?

• (g(x) * f'(x) - f(x) * g'(x)) / g(x)^2

• f'(x) / g'(x)

• f(x) * g(x)

• f'(x) * g(x) + g'(x) * f(x)

What is the value of h'(4) if f(4) = 2, g'(4) = 2, g(4) = 1, and f'(4) = 3 using the quotient rule?

• 2

• 1

• 0

• -1

What is the chain rule used for in differentiation?

• Finding the derivative of a product of two functions

• Finding the derivative of a composite function

• Finding the derivative of a sum of two functions

• Finding the derivative of a quotient of two functions

If h(x) = f(g(x)), what is the expression for h'(x) using the chain rule?

• f'(x) / g'(x)

• f(x) * g(x)

• f'(g(x)) * g'(x)

• f'(x) * g'(x)

What is the value of h'(4) if g(4) = 1, f'(1) = 2, and g'(4) = 2 using the chain rule?

• 5

• 2

• 3

• 4

Which rule would you use to differentiate h(x) = f(g(x))?

• Power rule

• Chain rule

• Quotient rule

• Product rule