1 / 14

12.4 Day 2

12.4 Day 2. Derivatives. Essential Question. How do I use the product and quotient rule to find a derivative?. Monomial: derivative of a product. Example 1 - Find the derivative of the function g ( x ) = 2 x 3 (5 x – 3). ALWAYS DISTRIBUTE THEN FIND THE DERIVATIVE OF THE PRODUCT FIRST.

charlesamy
Download Presentation

12.4 Day 2

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related