Mr. Miehl

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Presentation transcript:

Mr. Miehl miehlm@tesd.net The Product Rule Mr. Miehl miehlm@tesd.net

Objective To use the product rule for differentiation.

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.

This function consists of 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 Take each derivative NO! Does ?

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

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. This is the derivative!

The Product Rule

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

The Product Rule The derivative of a product is… the first times the derivative of the second plus the second times the derivative of the first.

The Product Rule

The Product Rule

The Product Rule

The Product Rule

The Product Rule

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.