Product & Quotient Examples

Business Calculus · Axiom Academy

EXAMPLE Product & Quotient Examples Step-by-step worked examples using the product and quotient rules "First times derivative of second, plus second times derivative of first" "Low d-high minus high d-low, over low squared" Find the derivative of f(x) = x² · eˣ Find the derivative of h(x) = (3x + 1)(x² - 4) Find the derivative of f(x) = (x + 1)/(x - 1) Find the derivative of g(x) = x²/(3x + 2) Product Rule: When you have multiplication that can't be easily expanded Quotient Rule: When you have a fraction with x in both numerator and denominator Neither: Sometimes it's easier to rewrite (e.g., x²/x = x, or expand the product first) Based on the example above, which approach is correct?

This is the written version of the interactive lesson above. See the full Business Calculus course.