Calculus I: Derivatives of Polynomials and Natural Exponential Functions (Level 3 of 3)

The video tutorial covers basic derivative rules and emphasizes the importance of rewriting functions into derivative-friendly forms using algebraic techniques. It provides examples of finding derivatives for various functions, including polynomials, radical functions, and rational expressions. The tutorial highlights the need for simplification before applying differentiation rules and prepares students for learning more advanced rules like the product rule.

Which rule is NOT mentioned as a basic derivative rule in the introduction?

• Constant Multiple Rule

• Product Rule

• Power Rule

• Sum and Difference Rule

What is the derivative of the function f(x) = x * sqrt(x) after rewriting it into a simpler form?

• 3/2 * sqrt(x)

• 3x^(1/2)

• x^(3/2)

• 2x^(1/2)

How can the function f(x) = (x^2 + x + 3) / x be rewritten to apply derivative rules?

• x^2 + 1/x + 3

• x + 1 + 3x^(-1)

• x^2 + x + 3

• 1/x + 3x

What is the final derivative of the function f(x) = (x^2 + 4x + 3) / (x^(2/5))?

• 8 * (x^(3/5)) / 5 + 12 / 5 * (x^(2/5)) - 6 / 5 * (x^(5/5))

• 8 * (x^(3/5)) / 5 + 12 / 5 * (x^(3/5)) - 6 / 5 * (x^(7/5))

• 8 * (x^(3/5)) / 5 + 12 / 5 * (x^(2/5)) - 6 / 5 * (x^(6/5))

• 8 * (x^(3/5)) / 5 + 12 / 5 * (x^(2/5)) - 6 / 5 * (x^(7/5))

What is the first step in simplifying the function f(x) = (x + 3)(x^2 - 5x + 2) to find its derivative?

• Distribute the binomial to the trinomial

• Apply the power rule directly

• Factor the expression

• Use the product rule

What is the final derivative of the function f(x) = (x + 3)(x^2 - 5x + 2)?

• 3x^2 - 4x - 13

• x^2 - 4x - 13

• 3x^2 + 4x + 13

• 3x^2 - 5x + 2

Which rule will be introduced in the next video to handle more complex functions?

• Quotient Rule

• Chain Rule

• Product Rule

• Implicit Differentiation