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Mastering Product and Quotient Rule in Derivatives

Learn how to apply the product and quotient rule to find derivatives of functions, including monomials and polynomials. Practice examples included.

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Mastering Product and Quotient Rule in Derivatives

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  1. 12.4 Day 2 Derivatives

  2. Essential Question • How do I use the product and quotient rule to find a derivative?

  3. Monomial: derivative of a product Example 1 - Find the derivative of the function g(x) = 2x3 (5x – 3). ALWAYS DISTRIBUTE THEN FIND THE DERIVATIVE OF THE PRODUCT FIRST

  4. Constant, Constant Multiple of a Power, and Sum and Difference Rules Simplify. Divide each term in the numerator by x. SIMPLIFY Monomial: derivative of a quotient Example 2 - Find the derivative of the function Divide each term by the MONOMIAL denominator

  5. Find the derivative of . A. B. C. D. Monomial: COMBINED

  6. Polynomial: Derivative of a Product • Example 4 Option 1: Use the Product Rule Find the derivative of the functionh(x) = (x2 – 2x + 3) (x3 – 4). Let f(x) = x2 – 2x + 3 and g(x) = x3 – 4

  7. = 5x4 – 8x3 + 9x2 – 8x + 8 Simplify.

  8. Polynomial: Derivative of a Product • Example 4 Option 2: Distribute and Find the derivative Find the derivative of the functionh(x) = (x2 – 2x + 3) (x3 – 4). = x5 – 2x4+ 3x3 – 4x2 + 8x – 12 Distribute = 5x4 – 8x3 + 9x2– 8x + 8Derivative

  9. Example 5 Find the derivative of the function. Quotient Rule Polynomial: Derivative of a Quotient Let f(x) = 4x3 and g(x) = x2 – 2. So,

  10. Substitution Distributive Property Simplify

  11. A. B. C. D. Polynomial: Derivative of a Quotient Example 6 Find the derivative of the function.

  12. HW: 12.4 Day 2 Worksheet

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