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Mastering the Product Rule for Differentiation

Learn how to find derivatives using the product rule, especially useful for functions containing two separate pieces multiplied together. Follow step-by-step instructions and examples for better understanding.

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Mastering the Product Rule for Differentiation

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  1. The Product Rule Complete the warm-up on your notesheet

  2. Objective • To use the product rule for differentiation. • TS: Making decisions after reflection and review

  3. The Product Rule Good News: Right now you can find the derivative of functions like … A number multiplied by a variable raised to a power. Bad News: The Power Rule doesn’t work for a lot of derivatives.

  4. The Product Rule This function consists of two separate pieces multiplied together

  5. The Product Rule What is the derivative of this function?

  6. The Product Rule Take each derivative NO! Does ?

  7. The Product Rule The derivative of a product is not equal to the product of the derivatives.

  8. The Product Rule • The derivative of a product must by calculated using the product rule:

  9. The Product Rule 1. Imagine that the function is actually broken into 2 pieces.

  10. The Product Rule 2. Leave first piece alone and derive second piece.

  11. The Product Rule 3. Add: Leave second piece alone and derive first piece.

  12. The Product Rule This is the derivative!

  13. The Product Rule Example A:

  14. The Product Rule

  15. The Product Rule Examle B

  16. The Product Rule

  17. The Product Rule Example C

  18. Conclusion • Remember: The derivative of a product is the first times the derivative of the second plus the second times the derivative of the first.

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