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

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Presentation transcript:

The Product Rule Complete the warm-up on your notesheet

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

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

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

The Product Rule What is the derivative of this function?

The Product Rule Does ? NO! Take each derivative

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

The Product Rule  The derivative of a product must by calculated using the product rule:

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

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

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

The Product Rule This is the derivative!

The Product Rule Example A:

The Product Rule

The Product Rule Examle B

The Product Rule

The Product Rule Example C

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.